Turbulence

A neural turbulence closure defines a new boundary-value problem, $R(U)=N(U)+F(U)=0$, with a coupled Jacobian $J(U)=N'(U)+F'(U)$, where $N$ is the original mean-flow operator and $F$ the learned closure. We establish two consequences of global tangent dissipation. For a monotone original operator, a positive uniform margin supplied by the original operator and closure together guarantees existence, uniqueness and a global inverse-sensitivity bound relating a posteriori solution error to the a priori residual. For a general original operator, a dissipative closure cannot worsen tangent dissipation, but this alone does not guarantee uniqueness. Tangent dissipation depends on both diffusion and reaction. We study two complementary ways to promote it: (1) an exact-integral construction enforcing non-negative tangent diffusion while leaving reaction unconstrained, and (2) a penalty on tangent-reaction violations at sampled states. Tangent diffusion enters the Jacobian, and non-negative secant eddy viscosity alone does not control its coercivity. We conduct tests with channel flow at $Re_τ=180$--$5200$, which provides a strongly monotone baseline. Both constrained closures reach accurate solutions in all 50 training-seed/Reynolds-number cases. At $Re_τ=1000$, we conduct tests with 10,000 starts for one fixed network per closure and we find one root for each constrained closure and multiple roots for the other closures. Although this does not prove uniqueness, it provides strong empirical evidence for uniqueness of the tested constrained closures. At $Re_τ=5200$, the construction and penalty reduce the reported inverse sensitivity relative to the original operator by approximately $372\times$ and $11\times$, respectively.

Numerical simulations reveal how vortices stretch and transfer energy, but establishing smooth evolution requires bounds that remain valid beyond the simulated resolution. Here I develop a computer-assisted framework that establishes global regularity for continuous families of three-dimensional periodic Navier-Stokes flows. Its central construction combines finite reference trajectories with a common error bound that covers an interval of centre fields and infinitely many smooth perturbation modes. The method retains the complete nonlinear residual before spectral truncation and controls the evolution until viscous decay guarantees regularity for all subsequent times. Applications to cyclic-shear, Arnold-Beltrami-Childress and three-component Taylor-Green fields yield explicit perturbation radii and include initial conditions outside the direct Fourier-Wiener smallness criterion. A parameter-uniform extension covers a connected family of non-Beltrami Taylor-Green centres without repeating the proof for individual parameter values. An ensemble of 4,096 configurations, supplemented by 1,600 refinement trajectories and public turbulence data, connects the mathematical observables to spectral transfer and vortex geometry. Matched neural-operator experiments show that physics-informed training improves physical prediction, while also revealing that these gains do not necessarily improve the discovery of proof-limiting initial conditions. Together, these results provide a reusable method for establishing regularity across prescribed flow families and a quantitative setting for evaluating how learned predictions can assist rigorous computation.

Graph-based surrogate models offer a promising route to accelerate computational fluid dynamics (CFD) simulations on unstructured meshes. However, their development is limited by the scarcity of benchmark datasets spanning multiple flow regimes and standardized protocols for long-horizon autoregressive prediction. We introduce ONECYL (ONE CYLinder), a new benchmark for unsteady flow past a circular cylinder across laminar, transitional, and high-Reynolds-number regimes. The benchmark comprises 450 high-fidelity Variational Multiscale finite-element simulations (270,000 flow snapshots) with randomized cylinder geometries, providing time-resolved velocity and pressure fields together with mesh connectivity, geometric descriptors, Reynolds numbers, and integrated aerodynamic quantities. Beyond the dataset, ONECYL establishes a unified evaluation framework combining full-field rollout errors, virtual probes, and drag and lift predictions to assess numerical accuracy and physical fidelity. To accompany the benchmark, we develop a Graph Transformer as a reference baseline predicting velocity and pressure fields autoregressively on unstructured meshes. Using ONECYL, we investigate geometric representations and physics-based regularization across the three Reynolds-number regimes. The results show that explicitly encoding the cylinder geometry through a level-set representation consistently improves long-horizon prediction accuracy and generalization to unseen geometries, while divergence-based regularization becomes increasingly beneficial as flow complexity increases. The ONECYL benchmark and its Graph Transformer baseline provide a reproducible framework for evaluating graph-based surrogate models and establish a foundation for future research on long-horizon prediction of unsteady bluff-body flows.

Accurate prediction of unsteady separated flows is challenging because the aerodynamic loads depend on nonlinear separation and vortex-shedding dynamics. Although high-fidelity CFD resolves these mechanisms, its cost limits repeated use in design and control. Standard field-level surrogate training, however, does not distinguish the flow regions that contribute most strongly to the aerodynamic loads. We introduce VATO (Vortex-Force-Aware Transformer Operator), which couples the Vortex Force Map (VFM) method to a geometry-aware neural operator through two complementary mechanisms. VATO-S adds training-only supervision of the local VFM force-contribution field, with no increase in model size or inference cost. VATO-A uses VFM contribution and sensitivity fields to prioritise force-relevant source locations for residual cross attention. The methods are evaluated on unsteady CFD data for double-edged-plate aerofoils over 54 trajectories from nine geometries. Over lead times of 1-20~ms, VATO-S reduces velocity, pressure, and vorticity errors by 10.4%, 1.0%, and 15.6%, respectively, while VATO-A achieves reductions of 15.8%, 7.5%, and 31.2%. VATO-S gives the lowest VFM-derived drag error, whereas VATO-A gives the lowest pressure-derived lift and drag errors. Over lead times extending 50% beyond the training range, VATO-A retains a 26.9% reduction in vorticity error and larger improvements in all four force readouts, despite reduced gains in velocity and pressure. These results show that force-aware operator learning can improve both flow-field prediction and aerodynamic functional accuracy in unsteady separated flows.

The downwash wake of a hovering quadrotor governs both the vehicle's own performance and the safe spacing of multi-rotor formations. Prior measurements have largely characterized the mean flow, using single-point anemometry, volumetric tracking, or planar cuts through part of the rotor system. Higher-order turbulent statistics of the merged wake, and how they relate to canonical jet scaling, have remained unresolved, particularly for small quadrotors at the low-Reynolds-number end of the size range. Here, we present a detailed particle image velocimetry (PIV) study of the downwash of a hovering Crazyflie 2.1 quadrotor (arm length, $l = 46$ mm), sampled along a diagonal cut, passing through rotors along the symmetry axis of the quadrotor, and a front-rotor cut, passing through adjacent rotors. The four rotor jets merge into a single column by $z/l \approx 5$, beyond which the mean velocity profiles progressively approach the canonical round-jet self-similar form, collapsing by $z/l \approx 13$ when scaled by the local centerline velocity and half-width. Centerline decay and half-width growth follow canonical scaling laws with an effective source diameter $D_\text{eff} = 2.29\,l$, effective Reynolds number $Re_{D_\text{eff}} = 3 \times 10^4$, at the low end of the range over which canonical jet scaling has been established, and spreading and decay constants nonetheless within the canonical round-jet range. Resolving both cuts shows that the turbulent normal stresses retain a bimodal, cut-dependent signature of the four-rotor source throughout the measurement domain.

In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures induce complex boundary conditions and fine-scale flow features that are difficult for standard neural networks to resolve. Conventional PINNs, even when combined with advanced training techniques, can suffer from a loss of accuracy and efficiency as the number of perforations increases. One important source of this difficulty is the soft enforcement of boundary conditions through penalty terms, which can lead to stiffness, gradient conflicts, and poor resolution of near-boundary flow structures. Hard constraints provide an alternative by encoding boundary conditions exactly into the network ansatz, but may introduce undesirable non-local effects due to the global nature of the approximation. To address these challenges, finite basis PINNs (FBPINNs), which are based on domain decomposition and localisation principles, are used together with hard boundary constraints that efficiently encode perforation-related boundary conditions. This approach helps mitigate spectral bias, improves overall accuracy, and exhibits convergence that is only weakly affected by the number of perforations, thereby providing an efficient and highly parallelisable neural network framework. The proposed approach is further supported with theoretical arguments, specifically focusing on the localisation and approximation properties of FBPINNs.

High-fidelity immersed-boundary simulation resolves the coupled motion of a deforming swimmer and its surrounding flow, but the resulting cost limits repeated evaluations for engineering design, parameter studies, and control. We develop neural-operator surrogates for temporal prediction of the hydrodynamic fields generated by planar and volumetric eel swimmers. The surrogates are trained on regular-grid fields exported from adaptive fluid--structure simulations and are conditioned on swimmer geometry and Reynolds number. The planar model jointly predicts two velocity components, scalar vorticity, and pressure. On five held-out high-Reynolds-number trajectories, its full-domain global relative L^2 error is 3.51 %. The volumetric formulation uses three target-specific models with a common multichannel input: one model predicts three-dimensional velocity, one predicts vorticity, and one predicts pressure. Their full-domain global relative L^2 errors on five held-out within-range trajectories are 3.44 %, 5.58 %, and 19.2 %. Together, the results demonstrate the feasibility of field-resolved neural surrogates for moving-boundary swimmer flows while identifying pressure accuracy and physical consistency as priorities for further development.

Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive. Recent advances, such as Diffusion Graph Networks (DGNs), have combined diffusion models with graph neural networks to sample equilibrium states directly from unstructured meshes, enabling distributional accuracy even from short simulations. However, graph-based diffusion approaches suffer from hand-crafted architectural constraints, limited receptive fields in message passing, and costly multi-scale designs, which restrict scalability to larger and more complex domains. We propose Fluid-DiT, a Graph-Free Diffusion Transformer that replaces graph message passing with attention-based denoising, eliminating explicit graph design while preserving the ability to model distributions of chaotic flows. Our framework introduces a latent-space formulation that disentangles geometric fidelity from distributional learning, reducing high-frequency artifacts and accelerating sampling. By leveraging the transformer's global receptive field, Fluid-DiT naturally captures both local flow structures and long-range correlations without requiring hierarchical graph coarsening. On canonical benchmarks including laminar cylinder wakes, ellipse-flow systems, and turbulent 3D wing experiments, Fluid-DiT consistently outperforms graph-based diffusion baselines in both sample quality and distributional accuracy, achieving higher $R^2$ correlations and lower Wasserstein distances. Moreover, it generalizes robustly from short, incomplete trajectories to unseen Reynolds numbers and geometries, demonstrating strong scalability.

Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.

The development and testing of advanced aerial robots require experiments in controlled environments with tailored airflow profiles. This paper presents an online learning algorithm for controlling the complex airflow field in a multi-fan vertical wind tunnel. Our method combines a simplified physical model with iterative, measurement-based learning, enabling sample-efficient convergence to desired airflow distributions. We demonstrate the method's versatility by generating complex airflow, such as uniform, Gaussian, and parabolic profiles. Crucially, we show that our algorithm can produce an airflow profile specifically designed for passive soaring, greatly enhancing flight performance of a soaring robot. Variability, practical utility, and robustness of our approach are further highlighted by successful operation with a varying number of fans.

Reliable forecasting of nonlinear physical systems underpins scientific discovery and engineering decision-making. Yet high-fidelity simulations are prohibitively costly, and machine-learning surrogates can be opaque and encode assumptions about system dynamics, limiting generalizability. Pretrained transformers mapping synthetic ODE trajectories to equations offer interpretable alternatives, promising transfer without system-specific equation knowledge. Transferring them reliably to high-dimensional physical data, however, remains an open challenge. We develop a verifier-guided (VG) workflow around ODEFormer as a symbolic backbone, using dynamical and physical-admissibility criteria to select from a multi-trajectory candidate equation pool, enabling transfer. On canonical Van der Pol oscillators, VG outperforms the original ODEFormer workflow across held-out initial conditions. We then address vortex shedding, a phenomenon occurring in atmospheric and plasma systems of societal relevance, through coordinate reduction and symbolic discovery at fixed and varying Reynolds numbers. VG discovers fixed-parameter reduced-order equations that recover the fundamental shedding oscillator and higher harmonics without a wake-specific candidate library or prescribed Navier-Stokes structure, while the cross-parameter model generalizes to withheld regimes. Reconstruction fidelity alone did not determine symbolic discoverability, highlighting the importance of compatibility between latent dynamics and the backbone's pretraining distribution. This work establishes a verifier-guided neural-to-symbolic methodology for interpretable and physically auditable forecasting in the natural sciences.

Autoregressive models accumulate error over long rollouts, yet at deployment there is no ground truth to measure it against. We train a single conditional latent diffusion model that steps a dynamical system forward or backward in time via a direction flag, and show that this bidirectionality supplies a measurement-free test-time error signal: rolling forward $i$ steps and then backward $i$ steps must return the model to its start, so the round-trip discrepancy $\mathcal{C}_i$ is a self-supervised proxy for the unobservable rollout error: no ensembles, no held-out data, no governing equations, for one extra rollout. We validate on compressible magnetohydrodynamics (MHD), an astrophysical turbulent radiative mixing layer, and natural face videos (CelebV-HQ). On held-out MHD trajectories, $\mathcal{C}_i$ ranks rollout error (Spearman $0.91$-$0.98$ at fixed depth; $0.69 \pm 0.16$ within trajectories), and a simple calibrator fit on training rollouts predicts its magnitude to within $1.14\times$ ($68\%$) and $1.29\times$ ($95\%$) with near-nominal coverage - one nat beyond a depth-only predictor, transferring to all six decoded physical fields. The same signal flags the out-of-distribution Orszag-Tang vortex (AUROC $0.98$; $1.0$ by depth $10$) exactly where sampling-dispersion baselines invert, and it cuts incurred error by $15\%$ at $80\%$ coverage - three times the depth-only baseline. Bidirectional training comes at negative cost, beating direction specialists in both directions, and the backward direction doubles as a fast inverse solver. On LE-PDE-UQ's turbulent Navier-Stokes benchmark, a single bidirectional model reaches accuracy within $1.3\times$ of their ten-model ensemble at a tenth of the training cost, with the best training-free pixel-level calibration. Round-trip consistency turns reversibility into a practical trust signal for generative models.

Predictive coding offers a powerful framework for cortical computation, yet scalable implementations that respect both Bayesian exactness and neurobiological constraints remain scarce. We bridge this gap by formally connecting predictive coding to Recursive Gaussian Processes (RGPs). RGPs employ a single Gaussian process $g(t, \cdot)$ indexed by layer index and input value, preventing the representational collapse of standard deep Gaussian processes while allowing learnable cross-layer dependence via $r_{1g}$. We demonstrate that RGPs intrinsically implement hierarchical Bayesian inference, uncertainty propagation, and precision-weighted prediction error. Critically, we map RGP components---the shared GP, spike-and-slab variable selection, and MCMC dynamics---onto the canonical cortical microcircuit, providing a neurobiological substrate for these computations. Drawing on the free energy principle, we show that RGP inference minimizes variational free energy, formally linking Bayesian mechanics to neuronal dynamics. Our synthesis positions RGPs as both a principled computational tool and a candidate model for the brain's predictive machinery, generating testable predictions for laminar-specific dynamics and spectral asymmetries between feedforward and feedback processing.

A flow surrogate validated on a simple regime is often taken as evidence that the approach will carry to a richer one. We test this assumption on two transient flows under time-varying boundary conditions emulating the process startup: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), a core semiconductor-manufacturing process, and the two-dimensional Karman vortex street (KVS) behind a cylinder. Eight surrogate models are compared on one shared evaluation pipeline, differing in whether they learn the full field or a latent representation, and whether they predict trajectories in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the process-relevant cumulative wall shear stress to 3.2% relative error. On the wake, a latent autoregressive DeepONet retains 96% of the shedding power that direct and one-shot models damp to almost zero. The deciding axis is the treatment of time. The self-sustained wake requires the phase memory that autoregressive feedback provides, while the boundary-driven film rewards a direct map. Pointwise RMSE picks the wrong model in both regimes, so the evaluation scores five physical questions instead, the field, its structure, invented motion, amplitude, and timing. The trained surrogates answer queries $10^3$ to $10^4$ times faster than the finite-element solver, but the offline cost of the training simulations means they pay off from the first query beyond the training set for CMP and the third for the KVS. The choice of surrogate should follow the dynamical character of the target flow, and its validation should use failure-mode-resolved metrics, since neither the winning architecture nor its validation transfers.

Approaching a target position and holding station in flowing water is a fundamental and critical capability for robotic fish operating in natural aquatic environments. Despite decades of advances in enhancing swimming efficiency and maneuverability, this capability remains underdeveloped, largely owing to the insufficiently characterized, highly nonlinear fluid-structure interactions inherent to freely swimming robotic fish in flows. To bridge this gap, we propose the SWiFT framework, a Swimming With Flow Toolbox that enables the efficient exploration of an egocentric station-holding policy for a body and/or caudal fin (BCF) robotic fish in unknown and turbulent background flows via reinforcement learning (RL). Our SWiFT integrates a free-swimming flow-tank experimental setup with a highly efficient, physically consistent computational fluid dynamics (CFD)-based simulator and a systematic sim-to-real transfer pipeline. The resulting policy achieves substantial improvements over state-of-the-art methods across all metrics, most notably root-mean-square error (RMSE) of distance. Furthermore, we validated that egocentric feedback alone, without any explicit flow sensing, enables station-holding in unknown turbulent flows, closely mirroring the biological phenomenon of rheotaxis. Accordingly, the success of this egocentric station-holding policy not only advances robotic fish control toward real-world deployment, but also highlights SWiFT's promise as a foundation for tackling complex swimming tasks for underwater robots.

A second order finite volume scheme rests on two local quantities: a gradient reconstructed in each cell, and a limiter which scales it down where the reconstruction would overshoot. Both are set by fixed formulas, and on coarse unstructured meshes a small network can supply better values. But a network is free to output anything, and the usual safeguard is a penalty in the training loss, which discourages inadmissible states without preventing them. We replace the penalty by a hard constraint. The network still sets both quantities, and every value it can produce lies inside safe bounds: its stencil weights cannot cancel a neighbour, and its limiter is capped by the local flow. The flux, the wall treatment and the time step are not learned and carry their own guarantees. Admissibility therefore holds for every value of the weights rather than as an outcome of training, and no negative density or pressure occurred in any computation reported here. Because the scheme is safe whatever the network does, we could ask what the network contributes. We test it on supersonic channel flow over an obstacle, including the forward facing step of Woodward and Colella. Learning lowers the error by 38% on an unseen geometry and 29% on an unseen obstacle topology, measured against the same scheme with the network switched off. The method aims at the accuracy of a fine mesh for the cost of a coarse one, and refining once improves the error fourfold while multiplying the run time by eight. Learning secures half of this improvement for a sixth of this time. All of this comes from one of the two quantities the network sets. The gradient reconstruction reproduces the full effect on its own, and the limiter accounts for about a tenth as much. This also explains why the gain fades beyond the Mach numbers the weights were trained on.

Autonomous robotic navigation in nonstationary time-varying fluid flows remains a fundamental challenge due to partial observability and the unpredictability of realistic environments. While classical optimal control frameworks employed in robotics require unrealistic a-priori global flow knowledge, biological systems are able to navigate successfully by exploiting localized sensory cues. In this work we present a reinforcement learning approach using the TD3 algorithm to train autonomous agents to reach arbitrary targets within a parametric, chaotic double-gyre flow. To investigate optimal sensory mechanisms, we evaluate five bio-inspired observation strategies based on relative position, local velocity or local vorticity measures, and short-term memory variants. Additionally, we analyze the impact of providing agents with explicit global flow parameters. Numerical results demonstrate that an agent that is able to sense and remember a set number of flow velocity measures achieves the highest performance. The experiments reveal a trade-off in sensor utility: velocity-aware agents optimize energy efficiency, whereas vorticity sensors provide superior structural mapping and achieve better target proximity. Incorporating explicit global flow parameters is shown to decrease navigation performance. This behavior suggests that reinforcement learning-based autonomous systems develop more robust and general policies when restricted to implicit flow representations. The presented results offer insights for improving the transition of bio-inspired robotic navigation from simulation to real-world environments.

Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state. While this saturated regime is of primary interest, direct numerical simulations must resolve the full transient dynamics before reaching it, incurring significant computational cost. In Computational Fluid Dynamics, reduced-order approaches such as Large Eddy Simulation mitigate computational cost by modeling small-scale dynamics, enabling tractable approximations of turbulent flows. In contrast, for systems such as gyrokinetics, comparably effective closures for the full dynamics are not generally available, and high-fidelity simulations remain necessary. Existing surrogate modeling approaches for these systems are autoregressive, hence they suffer from accumulating error. We instead propose to bypass explicit time evolution by directly modeling the distribution of saturated states under an ergodicity assumption, stating that ensemble averages over samples are equivalent to time averages of a single long simulation. We introduce GyroFlow, a latent generative model that directly estimates steady-state statistics of gyrokinetic turbulence in 5D phase space, without resolving the transient phase. GyroFlow generates saturated snapshots from noise, conditioned on dimensionless operating parameters and outperforms autoregressive, reduced-order, and other generative approaches, while providing substantial speedup. To evaluate generation quality we propose FGyD, a distributional metric computed in the latent space of a pretrained gyrokinetic model, and show that it correlates with downstream flux accuracy and solver convergence. Finally, GyroFlow can be used to warm-start the numerical code used to produce the data.

Closed-loop wall control learnt by multi-agent reinforcement learning can lower skin-friction drag in turbulent channels, but these gradient-based policies are trained on small periodic boxes and exhibit reduced performance when carried over to a larger domain. We recently showed that such policies are also prone to saturated bang-bang actuations that collapse into standing streamwise waves whose scale is set by the computational box rather than by the near-wall cycle, and proposed architectural fixes that avoid these degeneracies. Here, we employ Evolution Strategy (ES) to optimise a recurrent closed-loop controller directly on a large turbulent channel at $\mathit{Re}_τ\simeq180$, evaluating policy performance over full flow episodes using an energy-aware criterion and processing candidate policies in parallel. To our knowledge, this is the first application of an evolution strategy to the control of a turbulent flow. The ES controller reduces the skin friction by about $26\%$, exceeding the gradient-based multi-agent controller of Cavallazzi et al. (2026), GRU-MARL, trained on a minimal box ($17\%$), and marginally exceeding classic opposition control (OC, $22\%$). A wall-normal decomposition of the friction, Reynolds-stress profiles and anisotropy invariants show that the ES and opposition-controlled flows follow separate trajectories through the buffer layer, reaching comparable drag reduction by different reorganisations of the near-wall turbulence. In particular, the ES actuation correlates predominantly with the streamwise velocity fluctuations rather than with the wall-normal velocity that classical OC targets.

We present a physics-constrained machine learning framework for accelerating the direct numerical simulation (DNS) of turbulent reacting flows. The model replaces the direct evaluation of detailed chemical source terms with a surrogate that predicts reaction rates from a reduced thermochemical state. To improve physical consistency, the second law of thermodynamics is incorporated as a training constraint by enforcing non-negative entropy generation, which restricts the evolution of the thermochemical state to physically admissible directions and improves stability during time integration. The approach is demonstrated on DNS of a two-dimensional planar lean premixed methane-air flame interacting with a turbulent flow field. The model reproduces detailed-chemistry results with high fidelity while achieving more than an order-of-magnitude reduction in computational cost. Furthermore, a residual-based synthetic data augmentation strategy enables parametric exploration by constructing new training data from the original dataset, allowing accurate simulation at new inlet conditions without additional detailed-chemistry CFD runs. These results demonstrate that thermodynamically constrained machine learning can provide reliable and computationally efficient surrogates for detailed chemistry in high-fidelity combustion simulations.

Vision-language models (VLMs) are increasingly deployed on infrared (IR) remote sensing imagery in security-critical settings, yet their adversarial robustness remains unexamined. We present AirflowAttack, to our knowledge the first adversarial attack for IR remote-sensing VLMs and the first to weaponize thermal-airflow turbulence as the perturbation prior. A lightweight generator synthesizes a single input-agnostic perturbation regularized toward physically plausible airflow patterns. Optimized on one surrogate CLIP model, it attains a mean zero-shot scene-classification attack success rate (ASR, the fraction of samples whose top-1 class changes) of 48.5% across five diverse CLIP backbones, far exceeding four IR-specific physical baselines (27.7--37.0%). Applied to six state-of-the-art VLMs, it cuts scene-classification accuracy by up to 38.2% relative, yet paradoxically makes some models more confident in their IR analysis, confabulating the perturbation as genuine thermal evidence such as temperature gradients and convection. Ablations show the airflow prior raises physical plausibility at no measurable cost to attack success. Together with a benchmark spanning eleven models and four tasks, these findings expose critical vulnerabilities in the rapidly expanding IR VLM ecosystem.

We study the small-noise asymptotics of Euclidean heat regularizations of probability measures supported on manifolds with corners. Near a boundary or corner stratum, the relevant regime is a conical boundary layer in which the observation point approaches the stratum at the same scale as the Gaussian smoothing parameter. After rescaling this layer, the support is replaced to leading order by its inward tangent cone. We prove a two-term expansion for the heat-regularized density in this regime. The leading coefficient is the Gaussian mass of the linearized cone, weighted by the density on the support and by the adapted corner Jacobian; the first correction records the variation of the density, the Jacobian, and the quadratic geometry of the embedding. A localization argument then yields the corresponding expansion for the full heat regularization, with the nonlocal contribution exponentially small. From this density expansion we derive logarithmic asymptotics and uniform expansions for the score, the log-Hessian, and the scale derivative of the score. These formulas show how lower-dimensional support, boundary faces, corners, and curvature are encoded in the singular differential structure of small-noise Gaussian regularizations.

World models -- compressed latent representations of an environment that support action-conditioned prediction and planning -- are typically presented as a product of modern self-supervised learning. This paper argues that the functional anatomy of a world model was independently developed, deployed, and formally analyzed decades earlier in the model-order-reduction (MOR) and control literature, under different names and for a different purpose: the real-time operation of physical systems. We trace the anatomy across three communities. Low-dimensional models of turbulence built on proper orthogonal decomposition (POD) supplied latent dynamics learned from data of a chaotic environment; eigenface methods in early computer vision supplied the encoder-decoder half, including a primitive runtime validity check; and measurement-based POD frameworks for facility thermal control assembled the complete loop -- POD coefficients as latent state, parametric dependence on actuator setpoints as action conditioning, modal reconstruction as decoding, and, critically, a priori analytical error bounds as a verification layer that certified when the model's predictions could be trusted in closed loop. We then examine what each tradition possesses that the other lacks: MOR contributes verification, physical grounding, and extreme data efficiency; learned world models contribute nonlinear representation, transferability, and horizon. We argue that the outstanding obstacle to deploying world models in systems that cannot fail -- power, thermal, process control -- is not predictive fidelity but verifiability, and we outline a research agenda for physics-grounded, verifiable world models that unifies the two lineages.

Small multirotor aircraft are increasingly tasked with operations in the atmospheric boundary layer, where turbulent winds comparable to the vehicle's airspeed degrade trajectory tracking and can defeat conventional feedback control. This work illustrates a two-stage learning pipeline that first estimates the local wind from onboard kinematics and dynamics and then exploits that estimate inside a reinforcement learning (RL) flight controller. The wind estimator, an attention-augmented gated recurrent network trained on thousands of simulated flights through von Karman turbulence with power-law shear and veer, recovers the horizontal wind vector with a per-flight root-mean-square error of 0.40 m/s and a direction error of 3.2 degrees on unseen wind regimes, an accuracy near the floor imposed by unresolved turbulence, and generalizes to vertical ascent profiles with a skill score of 0.861 over a constant-wind reference. A proximal policy optimization controller receiving the frozen estimator's output reduces horizontal trajectory tracking error by 48% relative to a wind-blind proportional-derivative baseline across mean winds of 4 m/s to 12 m/s, winning on 100% of evaluation episodes. A three-way ablation decomposes this improvement into a kinematic component, available without wind information, and a wind-perception component; the perception share rises with wind speed, from small in light winds toward roughly half the total benefit in strong winds, consistent with the quadratic scaling of aerodynamic drag. The controller degrades gracefully on out-of-distribution winds of 13 m/s to 15 m/s, where the baseline fails catastrophically.

Extracting interpretable, localized physical mechanisms from complex spatiotemporal data is a foundational challenge across physics, biology, and engineering, but has remained out of reach on real measurements. The central obstacle is obtaining high-quality gradients of data via numerical differentiation, which amplifies noise, diverges for high-order equations, and falters on irregular geometries, limiting the scope of existing approaches to clean simulations of low-order systems. Here, we present weak dominant balance, a derivative-free framework that projects governing equations into a weak (integral) formulation, offloading differentiation onto smooth analytical test functions and leaving the data untouched. The method sustains accurate regime identification under severe noise where existing approaches categorically fail, delivers the first data-driven decomposition of a third-order partial differential equation applied to turbulent duct flow, and produces matching decompositions across direct numerical simulation and particle-image velocimetry measurements of a wavy channel flow, uncovering a previously uncharacterized dynamical regime. Weak dominant balance brings mechanism-level analysis out of simulation and onto measured data, and opens complex physical systems to direct, equation-grounded interpretation.

We discuss reasons why the scaling exponents of current Large Language Models (LLMs) applications are indicating an unsustainable regime in terms of energy resources. We further show that attributing the smallness of such exponents to a numerical bias due to the neglect of a non-zero value of the loss function in the limit of infinite data (``pedestal effect") does not remove the unsustainability issue. Finally, the effects of the smoothness (roughness) of the data on the scaling exponents is commented upon based on an analogy with phenomenological models of fluid turbulence.

Numerical simulations in industrial applications often require performing numerous high-precision computations parameterized by specific experimental conditions. For instance, in vehicle body design, aerodynamic simulations are essential for evaluating the aerodynamic characteristics of various proposed body geometries. However, computational resource constraints often become a bottleneck. Therefore, achieving the desired accuracy while minimizing computational cost is crucial. To address this challenge, model reduction methods have been developed to decrease the degrees of freedom by constraining the possible states of a physical system to a lower-dimensional subspace. In particular, reduction techniques that project the system onto a nonlinear subspace using neural networks have been actively studied. Our previous research developed a reduced-order model that integrates neural-network-based model reduction with a time-evolution method, implemented as a distributed parallel training framework to process high-resolution flow field data efficiently. In this study, we extend this reduction approach by incorporating a variational autoencoder to assess its robustness in high-Reynolds-number flows around multiple vehicle bodies with varying geometries. Specifically, we evaluate the reconstruction accuracy of vortex generation across different spatial and temporal scales using a compact latent representation, with a particular focus on the flow behavior near the rear end of the vehicle body.

Characterizing the complete wall-pressure spectrum in turbulent wall-bounded flows requires simultaneous access to the viscous-scale high-wavenumber content and the outer-layer low-wavenumber content -- a requirement that neither short-domain direct numerical simulation (DNS) nor sparse experimental measurements alone can satisfy. We propose Patched Flow Matching (Patched FM), a generative framework that fuses these two complementary sources by learning a patch-local prior over inner-scaled wall-pressure statistics from short-domain DNS and assimilating sparse sensor measurements at inference time through training-free posterior sampling. The patch-additive decomposition of the flow matching vector field decouples the generative prior from the global domain size, enabling reconstruction on domains arbitrarily larger than the training configuration. By expressing the patch prior in inner-scaled coordinates, where high-wavenumber wall-pressure statistics are approximately Reynolds-number invariant, the framework extends to higher Reynolds numbers through hierarchical transfer learning with as few as $500$ short-domain snapshots ($2.5\%$ of the base training data) at a fraction of the scratch-training cost. Applied to compressible channel-flow DNS at $Re_τ= 180$, $500$, and $1000$, Patched FM reconstructs full-resolution wall-pressure fields on a domain four times larger than the training configuration ($L_x^L = 16πδ$ versus $L_x^S = 4πδ$) from sensor coverage as low as $0.25\%$, recovering the low-wavenumber spectral content inaccessible to short-domain DNS with high fidelity in both streamwise and spanwise directions. Zero-shot generalization to unseen Reynolds numbers and ablation studies further confirm the role of inner scaling as a physical prerequisite for data-efficient Reynolds-number transfer.

High-resolution turbulence modeling is essential for scientific computing, but remains constrained by the cost of direct numerical simulation and the scarcity of full-resolution data. Existing scientific compressors reduce storage but typically operate on per-frame representations, whereas learned compressors yield compact latents that are often resolution-dependent and weakly aligned with the physics of turbulence. This raises the need for a compression framework that reduces data size, preserves physical diagnostics, and transfers from low-resolution training fields to high-resolution test fields without retraining. In this paper, we propose Physics-Preserving Latent Compression (PPLC), a patch-local latent compressor for three-dimensional turbulence. Motivated by inertial-range scale similarity, PPLC treats fixed-size patches as transferable units and applies a shared variational autoencoder independently of the global grid size. It combines exact mean preservation, zero-mean fluctuation encoding, an invertible Haar wavelet front-end, shift-consistency regularization, and overlap-aware reconstruction. Instantiated on forced isotropic turbulence, PPLC is trained only on stride-downsampled 256^3 fields and transfers zero-shot to 1024^3 fields. Experiments show that PPLC improves the balance between reconstruction accuracy and physical fidelity over classical and learned baselines, keeping diagnostics such as dissipation, enstrophy, energy spectra, and incompressibility closer to the ground truth. Beyond turbulence compression, PPLC offers a general strategy for physics-preserving latent representations that support data-efficient scientific surrogate modeling.

This paper presents Vortex, the multimodal video retrieval system developed by our team, FocusOnFun, for the Ho Chi Minh City AI Challenge 2025, designed to advance intelligent multimedia search and temporal reasoning. The system integrates adaptive keyframe extraction, multimodal metadata generation from vision-language and speech models, and a hybrid retrieval strategy that fuses CLIP and SigLIP2 embeddings through Reciprocal Rank Fusion to balance global and fine-grained semantics. To enhance interactivity, Vortex incorporates Rocchio-based relevance feedback and a multi-stage temporal search mechanism for sequential event alignment. Built on Milvus and Elasticsearch, the architecture enables scalable indexing and efficient retrieval. Evaluated in the official competition, our FocusOnFun team's system achieved a score of 79.6/88 (90.5%) in the Preliminary Round and was further evaluated in the Final Round, achieving an Excellent' overall performance with Outstanding' results in the question-answering (QA) task. This demonstrating the complementary strengths of CLIP and SigLIP2 and confirming the effectiveness of the hybrid retrieval approach. The system establishes a robust foundation for future research in intelligent, context-aware, and interactive video retrieval.

High-altitude Clear Air Turbulence (CAT) poses significant risks to aviation safety due to its unpredictability and challenges in detection. This study leverages machine learning models to improve CAT prediction within U.S. airspace at 200-350 hPa pressure levels, utilizing Pilot Reports (PIREPs), ERA5 reanalysis data, and aircraft aerodynamic parameters from the BADA database. Gradient boosting algorithms, particularly XGBoost, achieved the highest performance with an AUC of 0.904, demonstrating superior capability in capturing non-linear atmospheric dynamics. Key findings highlight the dominance of geographic coordinates (17.5% feature importance) and turbulence indices like TI3 in prediction, emphasizing the role of regional topography and upper-tropospheric instability. The integration of aerodynamic features such as drag force and wing loading improved the detection of moderate-to-severe perceived turbulence intensity (POD improved from 0.845 to 0.866), providing additional value to traditional aircraft-independent methods. Seasonal analysis revealed winter months as peak periods for CAT incidents, correlating with jet stream activity. While results align with global studies, limitations include geographic scope and aircraft-type diversity. This research underscores the potential of machine learning for operational CAT forecasting, with recommendations for future work focusing on global data integration and real-time telemetry to address climate-driven turbulence trends.

Evaluating neural operators for 3D turbulent flow requires validated datasets with physical benchmarks. We present a reproducible pipeline generating training data for 3D channel flows around generated geometries at Re=1,000-10,000. Our lattice Boltzmann solver with cumulant collision operators is rigorously verified against experimental measurements (Strouhal number, drag coefficients, turbulent fluctuations) with comprehensive grid convergence studies at resolution 1024x512x512. Building upon an established framework, this validated pipeline enables standardized surrogate model comparison. We outline planned systematic evaluation of Fourier Neural Operator and U-Net variants on forecasting, super-resolution, and error correction tasks, using physics-informed metrics to assess turbulent energy cascade representation. Future work will compare computational efficiency between numerical solvers and neural surrogates, exploring practical application. We seek community feedback on our validation approach, planned benchmark methodology, and evaluation priorities for neural operators in turbulent flows.

We propose a multiscale probabilistic reconstruction framework for hypersonic Couette flow, where near-wall states are inferred from limited top-wall observations using conditional diffusion model. The boundary layer is divided into overlapping wall-normal subdomains, and a single height- and Mach-conditioned Elucidating Diffusion Model (EDM) is trained jointly for M=6,7,8 to sample velocity, density, pressure, and temperature fields conditioned on a top-wall boundary slice. A soft overlap inpainting strategy assembles subdomain predictions into full-volume reconstructions while maintaining inter-subdomain continuity and small-scale variability. To improve the spectral fidelity of the generated fields, we introduce a novel bounded binned spectral power (BSP) loss that preserves high-wavenumber content while remaining numerically stable across the diffusion noise schedule. Validation against direct numerical simulation data shows that the model recovers instantaneous structures, spectra, statistical profiles, correlations, and wall quantities across all training Mach numbers, while providing spatially structured uncertainty estimates. The reconstructed Mach-conditioned profiles also collapse under the Trettel-Larsson transformation, indicating consistency with compressibility scaling. These results establish the domain decomposed conditional diffusion model with a bounded binned spectral loss as an effective probabilistic surrogate for near-wall reconstruction in hypersonic wall-bounded turbulence.

The ability to resolve complex physical phenomena with high fidelity and at low computational cost is central to addressing key challenges in modern engineering. A prime example lies in hypersonic flows, where the precise prediction of the full flowfield topology, in particular with respect to shock wave location and intensity, is critical. Yet supersonic and hypersonic flows continue to be a stumbling block for traditional reduced-order models and neural emulators that struggle to capture steep gradients in flow states with physical consistency in applications of industrial relevance. To that end, we introduce a fully GPU based workflow that integrates accelerated data generation with the training of neural emulators augmented by uncertainty quantification and physics-aware refinement. Our workflow is enabled by a differentiable high-fidelity solver (JAX-Fluids) which we employ for rapid dataset creation and residual-based improvement of the neural emulator to enhance physical consistency. Building on this framework, we first present a suite of model architectures and analyze their scaling behavior to expose their strengths and shortcomings. We then show that residual-based refinement enables training on cases where only mesh and input parameters are available, substantially reducing residuals and improving physical consistency. Together, differentiable simulation and residual-based refinement yield physics emulators that remain reliable beyond their training distribution, a key requirement for deploying surrogates in real-world engineering design loops.

Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this failure mode. On a 256^2 DNS dataset at Re_f \approx 2250, replacing an MSE-trained VAE with a zone-weighted log-spectral objective raises deep-dissipation retained spectral power from 25% to 94% in reconstruction and from 20% to 79% in unconditional generation. The improved latent representation also yields a substantially better sampling cost-fidelity tradeoff: the MSE-trained latent space imposes a fundamental quality ceiling near DD bias -0.70 that no integrator or step-count can overcome, while the spectrally regularized latent space reaches DD bias -0.117 at just 20 function evaluations. Mechanistically, encoder-decoder swap experiments show that the improvement is driven primarily by encoder-induced latent reorganization rather than decoder capacity, while a support-amplitude decomposition reveals that MSE-trained models behave as conservative suppression models, minimizing pointwise error by attenuating intermittent high-wavenumber structure. Both pipelines recover the second-order structure function and the correct sign of S_3, indicating the correct cascade direction without explicit supervision. A small residual gap in the magnitude of S_3 suggests that phase-coherent triadic organization remains a complementary axis to amplitude fidelity for future generative turbulence models.

Rendezvous is a critical task for multi-agent systems, requiring agents to coordinate to meet at an unspecified location. However, achieving this in fluid environments presents a challenge, as it remains unclear how agents can exploit underlying fluid kinematics to facilitate convergence. In this study, we adopt a multi-agent reinforcement learning (MARL) approach to develop physics-informed rendezvous strategies in vortical flows. Compared to a naive strategy, where agents navigate toward their counterparts, MARL strategies significantly improve the rendezvous rate. MARL strategies also show transferability across varying vortex intensities, vortex scales, and swarm sizes. By breaking the symmetry of the state-action map, MARL strategy leverages a non-intuitive mechanism that prevents agents from becoming trapped in separate vortices, thereby enhancing rendezvous success. Additionally, a heuristic strategy is extracted from the learned strategy and also outperforms the naive strategy. Furthermore, a theoretical analysis demonstrates that fluid deformation impedes the rendezvous process. Large finite-time Lyapunov exponents identify where fluid effects separate adjacent agents, suggesting that targets should be planned in weak-deformation regions. Our findings reveal the important role that agent-fluid interactions play in multi-agent tasks and highlight the MARL capability to explore swarm intelligence in complex flow environments.

We introduce scale-selective Proper Orthogonal Decomposition (POD) for transformer attention fields, inspired by the use of POD for extracting energetically dominant modes from turbulent flow ensembles. The Morlet continuous wavelet transform identifies dominant temporal scales in the attention lag structure across a document ensemble; POD then extracts the energetically dominant modes at each scale from the ensemble of attention fields. The resulting modes reveal layer-dependent scale organisation, with early layers emphasising fine scales and later layers shifting toward coarser scales. We define a spectral concentration index from the POD eigenvalue decay rate and show empirically that it differentiates layers by their attention field complexity. By the classical POD optimality theorem, the extracted modes minimise the average L2 reconstruction error over the ensemble (Theorem 1), giving a data-driven effective rank for each layer. The method requires no architectural modification and no linguistic annotations: dominant attention patterns emerge from ensemble statistics alone. The turbulence analogy is structural rather than physical: we borrow ensemble covariance and modal analysis, not fluid dynamics itself.

Sparse attention is becoming increasingly important for serving large language models (LLMs) as generation lengths continue to grow. However, deploying and evaluating new sparse attention algorithms at scale remains highly engineering-intensive, slowing both human researchers and AI agents in exploring the sparse attention design. To address this challenge, we present Vortex, a system that combines a Python-embedded frontend language atop a page-centric tensor abstraction for expressing a broad range of sparse attention algorithms, with an efficient backend tightly integrated into modern LLM serving stacks. Vortex enables rapid prototyping, deployment, and evaluation of sparse attention algorithms, effectively translating their theoretical efficiency gains into real-world throughput improvements. As a result, Vortex substantially accelerates the design and iteration of sparse attention algorithms. First, AI agents use Vortex to automatically generate and refine diverse algorithms, the best reaching up to $3.46\times$ higher throughput than full attention while preserving accuracy. Second, Vortex extends sparse attention to emerging architectures and very large models that are otherwise hard to experiment with, reaching up to $4.7\times$ higher throughput on the MLA-based GLM-4.7-Flash and $1.37\times$ on the 229B-parameter MiniMax-M2.7 on NVIDIA B200 GPUs.

A reinforcement-learning agent maximises its reward, which can diverge from the outcome its designer intended. In physical control the reward rarely closes that gap, and drag reduction in wall turbulence makes it concrete. A mass-conservation projection couples agents' outputs and erases the per-agent credit the policy gradient needs; a memoryless policy cannot resolve the slow near-wall cycle it acts on; and a pressure-gradient reward pays for nominal drag reduction by pumping power through the wall. Two degenerate controllers achieve large drag reductions while total dissipation rises, so the reported figure can mask a more wasteful flow. We trace each fault to its cause and fix it: a differentiable projection that restores credit, a recurrent policy with a widened sensing stencil, and a reward scored on the true wall power. The corrected controller acts on the flow within a closed energy budget, earning a conservative $17\%$ under honest accounting.

Flapping-wing aerial vehicles (FWAVs) demonstrate remarkable agility but face substantial autonomy challenges due to their high sensitivity to aerodynamic disturbances and limited sensor payload capacity. Current simulation platforms typically rely on oversimplified laminar flow assumptions and idealized sensor models, failing to capture the complex turbulence patterns and perceptual limitations encountered in real-world operation. This simulation-to-reality discrepancy significantly impedes the development of robust autonomy systems for FWAVs. We introduce FWAV-Sim, a high-fidelity Unity-based simulation framework that integrates: (1) a composite aerodynamic model combining quasi-steady blade-element theory with bluff-body drag effects, (2) spatiotemporally correlated turbulence generation through fractal noise synthesis, and (3) realistic sensor simulation including noisy IMU measurements, LiDAR point clouds, and RGB camera feeds. Our platform enables scalable generation of synchronized datasets containing ground-truth vehicle states, aerodynamic forces, turbulent wind fields, and multi-modal sensor streams. Experimental validation demonstrates that autonomy pipelines (including both controllers and perception systems) developed in FWAV-Sim exhibit significantly improved simulation capability, thereby advancing the outstanding performance in simulation-based development for flapping-wing aerial systems.

Accurate precipitation nowcasting is vital for disaster mitigation, but deep learning methods face a key trade-off: regression models produce over-smoothed, spectrally decaying predictions that blur convective details and violate turbulence power laws; diffusion models generate realistic yet unanchored hallucinations lacking physical grounding. We propose Spectral-Decoupled Iterative Refinement (SDIR), a deterministic framework that reformulates nowcasting as progressive frequency-decoupled refinement. SDIR first extracts a stable low-frequency synoptic skeleton, then iteratively refines high-frequency textures under physical constraints, eliminating both blurring and hallucinations. It features a dual-path design: the Synoptic Frequency-Guided Former (SFG-Former) with Scale-Adaptive Transformers for global structure, and the Fourier Residual Refiner (FR-Refiner) with Scale-Conditioned Fourier Neural Operators for fine residuals. A Physically Consistent Power Spectral Density (PCPSD) loss with dynamic masking enforces a turbulence-consistent spectral distribution. Experiments on three benchmarks show SDIR significantly outperforms SOTA methods in spatial accuracy while achieving spectral fidelity competitive with diffusion-based methods, enabling reliable high-resolution operational nowcasting. Code link: https://github.com/RuntimeWarning/SDIR.

Whether physics foundation models can be usefully deployed on laboratory experiments remains an open question for scientific machine learning (ML). We test this question on the Rayleigh-Taylor instability (RTI), a ubiquitous and demanding fluid instability seen from tabletop flows to supernova explosions, in which small perturbations at a density interface grow into chaotic, multiscale mixing as a lighter fluid accelerates into a heavier one. Standard ML models struggle with RTI, and despite over a century of theoretical, numerical, and experimental work, it carries an unresolved discrepancy between simulation and experiment: the late-time mixing growth rate, $α$, measured in most laboratory experiments ($\sim$ 0.06-0.07), is roughly three times the value from idealized direct numerical simulations (DNS, $\sim$ 0.02). The gap's origin remains debated. These properties make RTI a stringent test for a question that matters well beyond RTI: can foundation models trained only on simulations generalise to sparse, messy, and noisy laboratory settings? We finetune Walrus, a foundation model for continuum dynamics, on three or fewer DNS realizations and recover key RTI physics over long rollouts. Applied zero-shot to sliding-barrier laboratory data, the finetuned model leaves the DNS-like regime and enters the observed growth band, having never seen a single experimental sample. These results provide independent, data-driven evidence that initial conditions play a crucial role in the longstanding sim-experiment gap in $α$. The model also generalises zero-shot to stable stratification, a buoyancy regime absent from training, correctly slowing mixing-layer growth. Together, our results show that foundation models can generalise well beyond their training data, predicting laboratory behavior and unseen physical regimes, opening new ways to probe longstanding simulation-experiment gaps.

We propose a method combining Multi-Agent Deep Reinforcement Learning (MARL) and eXplainable Deep Learning (XDL) to reduce drag in wall-bounded turbulent flows. Taking as a baseline the results of training agents directly targeting wall-shear stress and opposition control, three SHAP-guided approaches are compared. In the first, the reward is computed from SHAP attributions of a U-net predicting the future velocity field; in the second, from SHAP attributions of a U-net predicting the skin-friction coefficient; in the third, from a combination of SHAP attributions of two U-nets predicting the skin-friction coefficient and the wall pressure fluctuations, respectively. The combined SHAP strategy based on skin-friction coefficient and wall-pressure fluctuations achieves the best overall performance, achieving a DR of 34.44% and a NES of 34.01% with only 0.43% normalized input power. Relative to opposition control, drag reduction and net energy saving increase by 49.41% and 48.52%, respectively. Compared with the direct wall-shear-stress baseline, the proposed strategy simultaneously improves performance while reducing the normalized actuation cost from 5.90% to 0.43%. Analysis of the results reveals that the energetically efficient policy is consistent with pressure-gated actuation, activating predominantly at near-zero wall pressure, and operates on a temporal timescale comparable to the lifetime of the near-wall turbulent structures.

In this work, we present our solution for the 8th UG2+ Challenge (CVPR 2026) Track 3: Dynamic Object Segmentation in Turbulence (DOST). Our method is built upon the strong baseline framework Segment Any Motion (SegAnyMo), which provides powerful mask generation and motion tracking capabilities. To further boost the segmentation performance under severe atmospheric distortions, we propose two key improvements. First, we employ a data-centric domain adaptation strategy. We significantly expand our training data by incorporating selected sequences from the DAVIS dataset alongside a subset of the DOST dataset, and apply simulated atmospheric fluctuation degradations to enhance the model's robustness against complex geometric distortions. Second, we introduce a spatio-temporal post-processing module. This refinement step effectively removes persistent boundary-connected false foregrounds and short-lived fragmented noise, while strictly preserving genuine small targets and maintaining original individual labels across frames. With these combined strategies, our proposed method ranks the 2st place in the challenge.

We argue that governance must transition from a normative discipline to an engineering discipline, and we develop a formal framework, inspired by the physics of metamaterials, to make this transition quantitative and testable. Artificial General Intelligence affects civilization primarily by increasing decision velocity while human verification capacity remains bounded. When the cost of validating AI-generated outputs exceeds the expected utility of acting on them, rational agents default to inaction: a stable but catastrophic Nash equilibrium we term the Freezing Equilibrium. Drawing on metamaterials, where emergent macro-properties arise from designed microstructure, we develop a phenomenological constitutive law for institutional coordination: $R_{\mathrm{eff}} = β\cdot (1-ρ) \cdot (1-τ) \cdot (1-γρτ)$, where $β$ is the decision branching factor, $ρ$ is provenance fidelity, $τ$ is the verification rate, and $γ\in [0,1]$ captures correlated-detection synergy between provenance and verification failures. The model predicts a sharp phase transition between self-healing ($R_{\mathrm{eff}} < 1$) and self-destabilizing ($R_{\mathrm{eff}} > 1$) regimes. We introduce a three-class provenance taxonomy: cryptographic, institutional, and context binding, and derive four falsifiable hypotheses with a proposed 12-week stepped-wedge cluster-randomized trial in government grant review panels. The framework bridges AI alignment theory and institutional design.

Real-time thermal-hydraulic simulation is essential for digital twin (DT) technology that supports the safe and efficient operation of small modular reactors (SMRs). Computational fluid dynamics (CFD) provides high-fidelity flow analysis, but its computational cost prevents direct use in DT applications. AI-based surrogate modeling has been actively investigated to address this limitation, yet neural operator--based surrogates for CFD-level transient analysis of SMR-specific geometries have not been reported. This study presents an integrated framework that combines a reduced-order model (ROM) with neural operators, applied to the helical coil steam generator (HCSG) of the System-integrated Modular Advanced Reactor (SMART). Two ROM strategies tailored to each CFD data type were compared, an MLP-based autoencoder (AE) for unstructured mesh data and a convolutional autoencoder (CAE) for structured mesh data, and each was coupled with the deep operator network (DeepONet) to construct the latent DeepONet (L-DeepONet). The Fourier neural operator (FNO) was additionally adopted for comparison. A multi-scale technique was incorporated into both frameworks to mitigate spectral bias and improve the prediction of Kármán vortex streets developing inside the HCSG. The multi-scale L-DeepONet captured the instantaneous periodic vortex dynamics in both velocity and pressure fields, while the FNO and its multi-scale variant predicted the time-averaged mean flow and provided reliable pressure drop estimates. These complementary characteristics provide a practical model-selection guideline that links each architecture to specific DT objectives based on CFD data type and the required level of flow resolution.

This technical report presents our solution for the CVPR 2026 UG2+ Challenge Track 3: Dynamic Object Segmentation in Turbulence (DOST). We design a training-free multi-signal segmentation pipeline that combines pretrained motion estimation, self-supervised semantic priors, background anomaly modeling, manually calibrated proposal fusion, and SAM2-based mask refinement. The method uses RAFT for dense motion responses, DINOv2 for semantic objectness priors, ViBe for training-free background modeling, and pretrained SAM2 for box-prompt mask refinement. Instead of optimizing an end-to-end segmentation network, our system operates entirely in inference mode. This design is suitable for the DOST setting, where severe atmospheric turbulence produces pseudo-motion, blur, and intermittent target visibility, making a single motion cue unreliable. The final submitted masks are evaluated by the official leaderboard, which reports 0.425041 mIoU and 0.457206 mDice. Since no task-specific model training or fine-tuning is performed, stronger learned temporal association, adaptive proposal selection, or task-specific adaptation may further improve the system.

Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span. Such linear methods struggle, however, for data with slowly decaying Kolmogorov $n$-widths, such as advection-dominated and turbulent flows, which require many modes for accurate reconstruction; moreover, energy-based truncation can discard low-energy modes needed to capture small-scale features. Recent nonlinear manifold methods using polynomial mappings with alternating or greedy mode selection achieve better reconstruction with fewer modes, but fix the form of the nonlinear mapping a priori, limiting expressivity. In contrast, neural network (NN) manifolds offer greater expressivity yet employ energy-based selection. We present SparseModesNet, a dimensionality reduction framework that employs linear encoding and nonlinear NN decoding. The decoder leverages LassoNet, a method enforcing hierarchical sparsity through a residual connection with a linear skip layer, to simultaneously select informative modes and learn a nonlinear mapping that minimizes reconstruction error. On benchmark advection-dominated and chaotic flows, SparseModesNet matches or exceeds state-of-the-art performance. For turbulent channel flow at friction Reynolds number $Re_τ= 5200$, our method reduces reconstruction error by 51-78% compared to existing polynomial manifold methods while maintaining interpretability through physically meaningful mode selection.

Turbulence is ubiquitous in engineering and science, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide savings exceeding ten orders of magnitude but introduce unclosed terms (the closure problem). Offline-trained machine-learning (ML) closures suffer distribution shift in predictive simulations, while ML methods that bypass the governing equations struggle to generalise from scarce high-fidelity data. We develop a physics-derived deep learning closure model for RANS, the Deep Algebraic Reynolds Stress Model (DARSM), which can be trained on small datasets and accurately generalise across Reynolds numbers, to unseen geometries, and to different flow regimes. A neural network maps flow invariants to empirical parameters in an implicit algebraic Reynolds stress equation, derived from the Reynolds stress transport equations under the weak-equilibrium assumption, imposing physics-based structure on the ML closure. End-to-end optimisation through the governing PDEs and the coupled implicit closure eliminates distribution shift, but both unrolled and implicit automatic differentiation fail on the stiff coupled solver. We derive adjoint equations that exploit the solver's implicit-explicit structure for efficient optimisation. On canonical square-duct and periodic-hill benchmarks, DARSM reduces average test velocity error over baseline RANS by $2$-$4\times$ across Reynolds number, geometries, and flow regimes, with peak case-level reductions of $12\times$. The model trained on attached, anisotropy-dominated flows (square duct) accurately generalises without retraining to separated flows (periodic hills), a regime change in the underlying physics. DARSM also outperforms five established ML methods: offline training, tensor-basis neural networks, field-inversion machine learning, DeepONets, and physics-informed neural networks.

Single-frame atmospheric turbulence mitigation is inherently ill-posed due to spatially varying blur coupled with non-rigid geometric distortion. Existing end-to-end approaches trained on flat-field simulations often struggle to balance texture recovery with geometric rectification. To overcome this limitation, we propose D$^2$Turb, a unified framework that bridges physics-grounded simulation with explicitly decoupled restoration. First, we introduce a Depth-Aware Turbulence Synthesis protocol that incorporates scene depth into the phase-to-space formulation. This generates physically consistent, depth-dependent degradations and provides a crucial intermediate tilt supervision signal for disentangled learning. Building upon this simulation engine, D$^2$Turb decomposes restoration into two interactive stages: texture deblurring and geometric rectification. The texture deblurring stage employs a deblurring backbone to recover fine-grained details while preserving geometric distortion for the subsequent rectification stage. To mitigate the information fragmentation commonly observed in cascaded designs, we further propose an Adaptive Structural Prior Injection (ASPI) mechanism that dynamically transfers deep structural representations from the deblurring module to guide dense flow prediction for spatial unwarping. Extensive experiments demonstrate that D$^2$Turb achieves state-of-the-art performance on both synthetic and real-world datasets, with consistent improvements in both texture recovery and geometric fidelity. Our code and pre-trained models are publicly available at https://github.com/HertzDot222/D2Turb.

This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While LNO captures transient and steady-state dynamics through learnable system poles and residues, it lacks an explicit mechanism for extracting spatially localized multi-scale features inherent in complex PDE solutions. WLNO addresses this by augmenting the LNO core with a parallel single-level Haar discrete wavelet transform (DWT) branch that decomposes the lifted feature map into four frequency subbands: approximation (LL), horizontal detail (LH), vertical detail (HL), and diagonal detail (HH) and applies independent learned $1\times1$ convolutions to each subband before reconstruction via the inverse DWT. The two branches are fused through a learnable sigmoid-gated weight $α_\mathrm{wav}$, initialized to give a small initial contribution to the wavelet branch, allowing the model to adaptively balance Laplace-domain dynamics against spatial multi-scale features throughout training. WLNO is evaluated against LNO on five benchmark PDE problems using identical hyperparameters, training data, and evaluation protocols: the diffusion equation, the Burgers equation, the reaction-diffusion system, Darcy flow, and the two-dimensional Navier-Stokes equation. WLNO consistently outperforms LNO on all five problems, with the most pronounced improvement on problems with strong spatial multi-scale structure, such as the Burgers equation with sharp shock fronts and the Navier-Stokes equation with coherent vortical structures, while remaining consistent across smoother and elliptic problems. These results demonstrate that wavelet-based multi-scale spatial decomposition is a principled and effective complement to Laplace-domain operator learning.

Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We introduce the Iterative Refinement Neural Operator (IRNO), which augments pre-trained operators with a learned refinement module iteratively applied via fixed-point iteration. IRNO decomposes the prediction into a coarse initialization followed by successive residual corrections, paralleling classical numerical solvers. Under local assumptions, we establish contraction of the induced operator, ensuring convergence to a unique fixed point. To explicitly target high-frequency errors, we propose a progressive spectral loss that adaptively increases penalty on high-frequency components over refinement steps during training. Across physical systems, IRNO consistently lowers error, with up to 56.05% improvement on turbulent flow. On Active Matter, spectral analysis reveals that, relative to base operator, the normalized error ratios decrease to 27.72-36.10% in low-, 5.07-6.68% in mid-, and 1.48-2.04% in high-frequencies, remaining stable beyond the trained iteration count. Code is available at https://github.com/xiaotianliu-dartmouth/Iterative_Refinement_Neural_Operator

Hard-label classification is usually trained with smooth surrogate losses, most prominently softmax cross-entropy. We isolate an asymptotic mechanism by which this mismatch between smooth surrogate and discrete labels produces power-law learning curves in an online teacher-student model. After subtracting the mean logit, the thermodynamic-limit dynamics close in centered variables: a growing centered student-teacher alignment $D$ and the residual student variance $Δ$. At late times, examples away from teacher decision boundaries are already classified confidently and contribute exponentially little. Only boundary layers of width $O(D^{-1})$ remain active, while the noise of fixed-learning-rate online gradient descent maintains a nonzero $Δ$. As a function of the training time $α$ the late-time solution yields a $α^{-1/3}$ power law not only for the test loss but also for the generalization error $ε_g$, i.e., one minus test accuracy. This is much slower than the $α^{-1}$ Bayes-optimal reference for the same model. We further show that learning-rate schedules can improve the generalization error towards a $ε_g \sim α^{-1/2}$ power law. Simulations support the predicted order parameter dynamics and learning curves. Controlled experiments with correlated Gaussian inputs and whitened pretrained features show that data structure can dominate transients. Therefore, our result is an asymptotic, complementary mechanism rather than an alternative to spectral explanations of neural scaling laws.

Earth Observation (EO) imagery is often degraded by atmospheric turbulence and pointing jitter; yet, these effects are rarely considered in datasets used to train AI-based detection models. Based on prior work, this paper presents an enhanced image simulator that enables the incorporation of vertical-path atmospheric turbulence and satellite pointing jitter, arising from platform and sensor vibrations, to generate physically realistic distorted images. As a case study, vessel detection is evaluated using YOLOv8 and RetinaNet on images generated by the proposed simulator under different levels of turbulence and pointing errors. Results show that YOLOv8 recall decreases from 91% under ideal conditions to 60% in the presence of weak turbulence, and falls below 40% under strong turbulence or jitter. In contrast, RetinaNet demonstrates greater robustness, maintaining approximately 75% recall across degraded conditions. These results highlight the importance of incorporating realistic physical degradations into EO training datasets to ensure reliable performance of AI-based models in operational environments, as demonstrated in maritime surveillance applications.

Standard transformer attention computes pairwise similarity between queries and keys, treating all tokens as equally salient regardless of their intrinsic informational content. In turbulent fluid dynamics, coherent structures -- the energetically dominant, spatially organized patterns that persist amid background chaos -- carry a disproportionate fraction of total energy and govern all transport. We propose that tokens play an analogous role in transformer attention: informationally dense positions (morphological boundaries, syntactic heads, discourse markers) concentrate spectral energy and should attract proportionally more attention than background tokens (function words, repeated patterns, low-information filler). We propose Energy-Gated Attention (EGA): a simple modification that gates value aggregation by the spectral energy of key token embeddings, computed by a single learned linear projection that discovers the dominant spectral mode of the embedding field. On TinyShakespeare, EGA achieves +0.103 validation loss improvement with only 12,480 additional parameters (<0.26% overhead) and no measurable computational cost. The result is consistent on Penn Treebank (+0.101), demonstrating dataset independence. A systematic ablation across three wavelet families (fixed Morlet, Daubechies db2/db4, and a parametric Morlet) establishes that fixed structured bases are suboptimal -- the optimal energy direction is data-adaptive and non-sinusoidal -- while identifying learned wavelet packets as a promising open direction. The learned energy threshold converges to tau ~= 0.35 independently of initialization, corresponding to the fraction (~36%) of tokens carrying above-average spectral energy in English text, a stable linguistic property consistent with the fraction of content words in running English text.

Atmospheric turbulence severely degrades video quality by introducing distortions such as geometric warping, blur, and temporal flickering, posing significant challenges to both visual clarity and temporal consistency. Current state-of-the-art methods are based on transformer, 3D architectures and require multi-frame input, but their large computational cost and memory usage limit real-time deployment, especially in resource-constrained scenarios. In this work, we propose ReMATF, a lightweight recurrent framework that restores videos using only two frames at a time while preserving spatial detail and temporal stability. ReMATF combines a multi-scale encoder-decoder with temporal warping and a motion-adaptive temporal fusion module that performs per-pixel fusion between the warped previous output and the current prediction to enhance coherence without enlarging the temporal window. This design reduces flicker, sharpens details, and remains efficient. Experiments on synthetic and real turbulence datasets show consistent improvements in PSNR/SSIM and perceptual quality (LPIPS), along with substantially faster inference than multi-frame transformer baselines, making ReMATF suitable turbulence mitigation in resource-constrained scenarios.

Long-horizon prediction of three-dimensional (3D) wall-bounded turbulence with machine-learning methods remains a challenging task, due to the rapid accumulation of autoregressive errors and the substantially computational cost. To address these challenges, we present a hybrid machine-learning framework, in which a channel-time-attention Swin-UNet (CTA-Swin-UNet) and a multi-time-scale fusion correction (MTFC) strategy are developed to predict the turbulent flow fields in a wall-parallel plane, with affordable computational cost. Then, 3D flow fields are reconstructed via a resolvent-based spectral linear stochastic estimation (SLSE), rooting from the predicted planar flow. Results show that the CTA-Swin-UNet outperforms the baseline models (LSTM, FNO and traditional Swin-UNet) in both single-step prediction and autoregressive rollouts, indicating the effectiveness of introducing the CTA module into the Swin-UNet architecture. At the same temporal interval, the CTA-Swin-UNet remains stable for approximately 150 rollout steps, while the baseline models fail within 20 to 50 rollout steps. After introducing the MTFC strategy, a longer horizon upto 300 steps is achieved. Using the resolvent-based SLSE reconstruction further recovers the 3D flow structures and energy spectral distributions from the predicted planar inputs, which demonstrates that the proposed framework provides an effective and computationally efficient approach for long-horizon autoregressive prediction of 3D wall-bounded turbulence.

Finding an odor source in a turbulent flow requires effectively leveraging the history of olfactory observations into a robust navigation strategy. In this work, we use tabular Q-learning to train an olfactory search agent with a minimal memory of past observations: only a running clock since the last whiff. This agent learns an interpretable strategy to recover the plume which combines well-known behaviors observed in insects: surging, casting, and a return downwind. While achieving good performance on data from direct numerical simulations of turbulence, the agent is limited by an inability to adapt its strategy to the local intermittency level; we show that providing more flexibility improves robustness.

Turbulent dynamical systems are characterized by nonlinear interactions and stochastic effects that generate coupled statistical quantities, such as non-zero higher-order moments, which are difficult to capture from data with accuracy. We propose a two-stage data-driven modeling framework that combines symbolic regression with generative models to jointly identify the governing dynamics and predict their key statistical quantities. In Stage I of the framework, the Finite Expression Method (FEX) is adopted to discover closed-form expressions of the deterministic dynamics, recovering nonlinear interaction terms and external forcing without predefined libraries. In Stage II, generative models are introduced to learn the residual stochastic components as a refined correction to the model error from the Stage I approximation, enabling accurate characterization of higher-order statistics. Theoretical analysis establishes the consistency of the symbolic estimator and quantifies the estimation error in terms of data size and numerical discretization. The model performance is verified through detailed numerical experiments on the stochastic triad models across multiple regimes, demonstrating that the framework successfully recovers interaction terms and forcing expressions, and accurately predicts statistical moments up to order five. These results highlight the potential of integrating interpretable symbolic discovery with data-driven stochastic modeling for complex turbulent systems.

This paper proposes Drain-Vortex Optimization (DVO), a population-based metaheuristic for continuous optimization. DVO models each candidate solution as a particle moving in a multi-drain vortex field. Its update rule decomposes motion into radial attraction toward selected drain centres and tangential rotation governed by a regularized free-vortex law. A three-phase mechanism switches between far-field exploration, spiral inward motion, and localized core exploitation according to the normalized distance to the assigned drain. The method also uses adaptive spiral exploitation, population-level vortex basin assignment, and optional stochastic basin switching to support structured diversity. DVO is evaluated against PSO, GWO, WOA, SCA, AOA, EO, and SVOA using a calibration--validation protocol. CEC 2022 is used only to select the final DVO configuration, while CEC 2017, classical functions, and five constrained engineering design problems are used for out-of-sample validation. On CEC 2017, DVO achieves the best mean $\log_{10}$ error on 34 of 58 cases and the best Friedman average rank (1.67), and is significantly better than every baseline under Holm-corrected Wilcoxon tests. On CEC 2022, DVO obtains the best Friedman rank (2.13) and is significantly better than five of the seven baselines; the differences against PSO and SVOA are not significant. DVO is less competitive on simple scalable classical functions and on small constrained engineering designs, which clarifies its operating regime. The algorithm is implemented in a vectorized GPU form that executes independent runs in parallel.