Queryable Sector Flow Fields

Flow matching generates samples by gradually transforming noise into data. In practice, using a finite number of sampling steps introduces a numerical error that depends on the chosen schedule. We study this dependence for Gaussian targets and the explicit midpoint sampling method, using the exact flow field. We measure sampling error by the squared Wasserstein distance between the target distribution and the final distribution produced by the midpoint sampler. We show that the standard conditional optimal transport (CondOT) schedule cancels the leading midpoint error and improves the general convergence bound, even when the sampling steps are unequally spaced. On a uniform grid of $S$ sampling steps, we fix the signal schedule at $α_t=t$ and prove the existence of scalar noise schedules $β_t$ that approach the CondOT noise schedule $1-t$ at rate $1/S$ and yield exact Gaussian sampling for every sufficiently large $S$. Controlled Gaussian experiments illustrate the convergence rates and exact calibration.

The kinematics of an articulated object is often ambiguous from vision alone. Interaction resolves the ambiguity, and active perception methods exploit this by searching for the single action that most sharpens a belief over the kinematic parameters at each step. Such greedy search cannot be extended over a horizon without forward models of the contact and inertial dynamics, which are themselves unknown. We instead amortize action selection into training. We maintain a belief distribution over joint type and parameters, initialized from a generative prior and updated by Bayesian filtering on the observed part motion. To condition the policy on this belief, we render it as a per-point articulation flow field, the motion that the current posterior predicts for every point on the object. Carrying the inductive bias of articulated motion, this representation generalizes better than a latent encoding of the belief or flow tracked from observation. We train the policy with reinforcement learning, rewarding the entropy that each interaction removes from the posterior, so that informative exploration becomes learned behavior rather than a search at every step. Our method outperforms previous approaches across door and drawer manipulation on the PartManip benchmark, and reaches 61.7% success on ArticuRiddle, a new dataset of objects whose appearance implies the wrong articulation, against 44.4% for the best previous method. Project Website: https://hiddenkinematics.github.io/

Spatial flow measurements support underwater navigation, but distributed sensing is constrained by robot size and sensor layout. We use a causal observer to estimate current lateral velocities from a finite history of measurements collected by a single sensing unit, supplying the inputs of a fixed navigation controller. In two-dimensional wake simulations with access to body-frame ambient velocity, this virtual sensing interface reduces simultaneous flow sampling from three points to the robot center. Trained only in a circular-cylinder wake at Re = 100, the flow-history observer achieves 84.4% and 80.6% success at held-out Re = 205 and 240 without retraining. These rates are 7.4 and 4.6 percentage points below direct spatial sensing and more than 30 points above a matched current-only observer. Past flow remains beneficial when past goal and yaw information is available. Across obstacle geometries, performance remains close to direct sensing in square-prism wakes but declines in triangular-prism wakes. Component replacement identifies the lateral velocity difference as control-relevant, while controlled perturbations reveal sensitivity to error persistence. The results demonstrate the closed-loop utility of single-point flow histories under the assumed observation model.

Closed-loop human-AI systems generate high-dimensional behavioural trajectories whose collective dynamics remain obscure. Using 297,915 learners' adaptive-tutoring histories, we define semantic order variables before model fitting and test them in user-disjoint cohorts. The state exhibits reproducible basin-like flow and operationally defined, state-heterogeneous metastable-like kinetics. A construction-matched null distinguishes normalised-memory relaxation from a reproducible excess field. A four-term conditional mechanism recovers population drift (r = 0.946; learner-bootstrap 95% CI, 0.935-0.955). Predictive event-level self-supervised learning recovers the state and learned-plane flow; null-referenced corrections retain directional, partial-amplitude excess-field structure without full calibration. Shuffled-order training reverses learned-plane flow on ordered trajectories; support-alignment randomisation selectively reduces inward transport. Both axes remain linearly accessible without state supervision. Without cross-model fitting, the models share leading population drift (r = 0.866; learner-bootstrap 95% CI, 0.857-0.875) and persistence ordering; residual directions remain model-specific. These results identify an externally anchored leading-order effective field linking empirical dynamics, an interpretable mechanism and neural computation.

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.

In stream finishing, the wear experienced by a workpiece depends strongly on its orientation within the rotating abrasive media. Determining suitable orientations to achieve uniform wear requires evaluating the wear-rate field over all feasible orientations. Although the discrete element method (DEM) accurately resolves particle interactions, simulating hundreds of feasible orientations for a new geometry is computationally expensive. We present an uncertainty-guided surrogate framework that predicts, directly from geometry, the three fields governing erosion: per-triangle normal impact velocity, tangential impact velocity, and particle impact flux. These fields are combined through the Finnie wear model to reconstruct the wear-rate distribution. The surrogate employs a deep ensemble whose disagreement estimates epistemic uncertainty, enabling an active-learning strategy that selectively performs DEM simulations for the most uncertain orientations. Trained using only $13\%$ of the $696$ feasible orientations, the surrogate achieves Spearman rank correlations of $0.93$, $0.89$, and $0.93$ for the normal impact velocity, tangential impact velocity, and particle impact flux, respectively. Moreover, the predicted uncertainty is well calibrated, reliably anticipating prediction error and the fidelity of the reconstructed wear field, which matches DEM with a Spearman rank correlation of up to $0.97$ for low-uncertainty orientations and degrades in a controlled manner as uncertainty increases.

Mobile robots can infer local flow structure from onboard sensing, but a locally plausible estimate is not always safe to write into a global map. Similar flow structures may produce ambiguous observations, while localization drift causes predicted patches to be written at incorrect locations. Repeated misregistered updates then accumulate into persistent ghost structures. We address this failure mode with a map-reference-aware conservative fusion framework. The model predicts a local velocity patch and a learned write-safety score that continuously attenuates uncertain map updates while permitting initialization when no reliable map reference is available. Across synthetic jet and crossflow environments, the proposed method reduces average ghost contamination by 42% relative to ungated fusion. A zero-shot hardware replay using real pressure and optical-flow measurements from a thruster wake further reduces ghost contamination by 39% while retaining 81% map coverage. These results show that safe map writing is critical for flow mapping under ambiguous sensing and localization drift.

Vision-Language Navigation has increasingly emphasized high-level instruction reasoning, memory, global map construction, and instruction decomposition, while the low-level action representation remains comparatively underexplored. We propose CoFL-S, a low-level vision-language-action framework that predicts a language-conditioned flow field over the robot's local visible sector and generates continuous trajectories by rolling out the predicted field. To train this low-level representation, we convert each VLN-CE episode, originally a whole-episode instruction paired with an action sequence, into frame-level local supervision with aligned sub-instructions and matched action, trajectory, and dense flow-field targets. For evaluation, we introduce a continuous-time Habitat benchmark that isolates low-level action interfaces from instruction decomposition and executes all methods through a shared velocity-command controller, enabling decomposition-independent closed-loop comparison across different planner frequencies rather than fixed discrete forward-and-turn transitions in VLN-CE. Under matched encoders and training settings, CoFL-S consistently outperforms action-token and action-chunk baselines across planner frequencies in the continuous-time Habitat benchmark, and zero-shot real-world closed-loop deployment further shows its advantage over both baselines beyond simulation.

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.

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.

While Computational Fluid Dynamics (CFD) provides high-fidelity flow fields for optimizing indoor environments, its computational cost limits rapid exploration. To solve this problem generative surrogates offer better distribution modeling than deterministic networks, but iterative sampling is slow. To enable high-quality, single-pass generation, we adapt the novel generative drifting framework to fluid mechanics. We introduce a conditional architecture that performs drifting in a learned VAE latent space and uses label-aware masking to align generated samples with their boundary conditions. Our label-conditioned model matches iterative diffusion in accuracy and flow consistency while running two orders of magnitude faster. Additionally, we propose a spatial-conditioning variant that establishes a promising path towards generalization to unseen geometries. Ultimately, conditional drifting serves as a highly efficient alternative to diffusion based approaches, unlocking real-time CFD surrogates where inference speed is critical.

Autonomous underwater vehicle (AUV) launch and recovery (LAR) into the hull of an advancing host platform requires traversal of a complex, three-dimensional propeller wake whose hydrodynamic structure cannot be characterised by a uniform current model. High-fidelity Reynolds-Averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) simulations resolve this structure with sufficient accuracy for path planning, but their computational cost renders them impractical for onboard use. We address this gap by integrating two conditional generative adversarial network (cGAN) architectures -- a regularised PatchGAN and a 2D3DGAN with self-attention -- as drop-in replacements for RANS CFD data within a three-dimensional, energy-weighted A* path planning framework. Both generators are driven by a hierarchical pipeline that synthesises full $128^3$ voxel flow field volumes from scalar operating condition inputs alone, with end-to-end inference times of approximately 28-146 $μ$s, compared to hours for a single RANS computation. We benchmark all four environmental knowledge levels: uniform current, ground-truth CFD, PatchGAN, and 2D3DGAN~SA across 19,800 independently generated trajectories spanning 550 distinct flow conditions. Full CFD wake knowledge reduces energy expenditure by 5.7-12.5% and high-velocity wake-core encounters by up to 77.8% relative to uniform-current planning, with both benefits scaling with operating severity. The cGAN surrogates recover approximately 45-60% of the CFD energy benefit and high-velocity cell avoidance benefit while operating at inference speeds compatible with edge device use. These results provide the first systematic quantification of the downstream path planning value of cGAN-predicted hydrodynamic fields in a three-dimensional maritime robotics application.

High-fidelity computational fluid dynamics is essential for aerospace design, but engineering-scale simulations of practical three-dimensional aircraft remain computationally expensive. Learning-based flow-field initialization can improve efficiency by reducing the numerical distance between the initial and converged solutions, yet existing deep learning approaches remain difficult to scale to large three-dimensional aircraft flows with multiscale regional heterogeneity. Most prior studies therefore focus on two-dimensional problems, surface quantities, integral aerodynamic coefficients, or simplified three-dimensional cases with limited grid resolution.Here we propose MHLF, a multigrid-hierarchical learning framework for accelerating engineering-scale aircraft flow simulations while preserving high-fidelity numerical accuracy. MHLF combines a topologically consistent geometric multigrid representation with a hierarchical strategy that captures regional flow heterogeneity during both prediction and subsequent CFD correction. Across three engineering-scale aircraft cases spanning Mach 0.15 to 6.0 and covering subsonic, transonic and supersonic regimes, MHLF accelerates convergence without sacrificing flow-field accuracy, achieving a 3 to 8 times efficiency improvement over conventional initialization. These results demonstrate practical full-flow-field prediction for large three-dimensional aircraft within the CFD domain and provide a foundation for data-driven acceleration of high-fidelity aircraft flow simulation.

Reconstructing flow fields from sparse measurements is a fundamental problem in fluid mechanics with broad implications for modeling, control, and design. In this work, we propose a novel operator learning framework that leverages the architecture of language models to perform flow reconstruction in a mesh-free manner. We reformulate flow field reconstruction as a sequence-to-sequence learning task, where sparse measurements are treated as context and unobserved locations as queries. Our model learns to reconstruct the full flow field from sparse inputs, effectively capturing spatial correlations and long-range dependencies. We evaluate the proposed approach on four benchmark datasets: (1) two-dimensional vortex street simulations, (2) daily average temperature data across the contiguous United States, (3) three-dimensional blood flow simulations based on dissipative particle dynamics, and (4) three-dimensional turbulent jet flow measurements obtained via particle tracking velocimetry. Across all cases, our method demonstrates competitive reconstruction accuracy, even with highly incomplete data (less than 10% observed), and achieves efficient performance. The results highlight the potential of language models as robust and scalable tools for scientific data reconstruction, and suggest a promising direction toward the development of foundation models for scientific and engineering applications.

Inferring unknown initial states in shock-dominated compressible flows from sparse and noisy measurements is a challenging ill-posed inverse problem due to nonlinear wave interactions and limited sensing. In this work, we develop a non-intrusive reduced-order modeling framework for efficient Bayesian initial-state inversion with uncertainty quantification. The framework combines a convolutional autoencoder with a learned latent-space forward operator. The autoencoder compresses high-dimensional flow fields into a compact nonlinear latent representation, while the forward operator predicts final-time latent states from encoded initial conditions. This AE-ROM surrogate enables rapid forward evaluations and is embedded within a No-U-Turn Sampler (NUTS) for posterior exploration. The framework is demonstrated using 500 high-fidelity Sod shock tube simulations generated through Latin hypercube sampling and solved using a fifth-order WENO scheme. The inverse problem seeks to recover unknown left and right density and pressure states from sparse noisy observations of final-time density and pressure fields. Results show that the AE-ROM accurately reconstructs key shock-tube structures, including the rarefaction wave, contact discontinuity, and shock front. A latent dimension of 32 provides an effective balance between reconstruction accuracy and reduced-space compactness, while 250 training simulations are sufficient for accurate reconstruction. Increasing observation density significantly contracts posterior uncertainty, reducing the mean posterior standard deviation by approximately 78% for density and 76% for pressure. Overall, the proposed framework provides a computationally efficient and uncertainty-aware approach for inverse analysis of shock-dominated flows, with potential extensions to multidimensional compressible-flow and digital-twin applications.

In dynamic flow fields, various animals exhibit remarkable odor search capabilities despite relying on stochastic detections. Interestingly, there exists an optimal time window for integrating these detections that maximizes search efficiency. To understand the underlying mechanism, we investigate the navigation performance of Reinforcement Learning (RL) agents in unsteady flows under varying memory lengths and flow conditions. Without any predefined models, the agents develop a flow-assisted casting strategy and adaptively adjust both the geometry of their search trajectories and the concentration threshold for initiating casting to maximize the success rate. The agent's average speed toward the odor source exhibits a non-monotonic dependence on memory length, which can be explained by the "sector-search" model.

Reconstructing continuous flow fields from sparse surface-mounted sensors is central to aerodynamic design, flow control, and digital-twin instrumentation. Existing neural methods for this task typically encode sensor readings into implicit latent codes with little spatial interpretability and limited formal guidance on how representational capacity should scale with observation count. Inspired by 3D Gaussian Splatting, we introduce FLUIDSPLAT, a sensor-conditioned model that predicts K anisotropic Gaussian primitives forming a partition-of-unity scaffold, a spatially explicit and interpretable intermediate representation of the flow. For an idealized Gaussian primitive estimator, we prove an $O(K^{-s/d})$ approximation rate for fields with Sobolev smoothness $s$; incorporating $N$ noisy observations yields a squared-risk decomposition with bias $O(K^{-2s/d})$ and variance $O(σ^{2}K/N)$.Balancing the two yields $K^{*}\!\sim\!(N/σ^{2})^{d/(2s+d)}$: primitive count cannot grow freely under sparse sensing, revealing a variance bottleneck that motivates complementing the scaffold with a state-conditioned residual decoder. Across four benchmarks spanning 2D and 3D, FLUIDSPLAT achieves 11-28% error reduction over several strong baselines on cylinder flow, AirfRANS, FlowBench LDC-3D, and PhySense-Car 3D benchmarks.

This study investigates active flow control (AFC) of a 30P30N high-lift wing at a Reynolds number Re$_c$ = 450,000 and angle of attack $α$ = 23$^\circ$ using wallresolved large-eddy simulations (LES). Two optimization strategies are explored: open-loop Bayesian optimization (BO) and closed-loop deep reinforcement learning (DRL), both targeting the mitigation of stall and the improvement of aerodynamic efficiency via synthetic jets on the slat, main, and flap elements. The uncontrolled configuration was validated against literature data, confirming the reliability of the LES setup. The BO framework successfully identified steady jet velocities that increased efficiency by +10.9% through a -9.7% drag reduction while maintaining lift. In contrast, the DRL agent, despite leveraging instantaneous flow information from distributed sensors, achieved only minor improvements in lift and drag, with negligible efficiency gain. Training analysis indicated that the penalty-dominated reward constrained exploration. These results highlight the need for carefully designed rewards and computational acceleration strategies in DRL-based flow control at high Reynolds numbers.

Designing photonic integrated circuits requires accurate electromagnetic field simulations, which remain computationally expensive even for simple device geometries. We present PIC-Flow, a generative neural surrogate that predicts electromagnetic field distributions for photonic devices given their geometry and operating wavelength as an alternative to costly finite-difference time-domain (FDTD) simulations. Our approach combines three key ideas: (i) conditional flow matching as the generative framework, learning a velocity field that transports Gaussian noise to physically valid field solutions; (ii) a real-valued U-Net operating on split real and imaginary field channels; and (iii) physics-constrained training through a Helmholtz residual loss enforcing $\nabla^2 E_z + k_0^2 \varepsilon E_z = 0$. We introduce an interface-aware masking scheme for the Helmholtz residual that excludes dielectric boundary pixels where finite-difference stencil errors dominate, yielding a physically meaningful compliance metric. The data set consists of 22,500 ground-truth FDTD simulations split evenly between multimode interferometers, Y-branches, and directional couplers at $λ=1.55\,μ$m in an 80/10/10 split between training, validation, and test sets. We evaluate ablations on the network against the held out test devices and also show that the model generalizes to held out device classes such as S-bends, tapers, and cascaded Y-branches. Rather than a drop-in replacement for FDTD, this work establishes a foundation that, with broader data coverage, more compute, and further training optimization, could scale toward broadband, device-agnostic field prediction with dramatically improved runtime for rapid design-space exploration of complex photonic devices and circuits.

High-fidelity CFD is essential for aerodynamic design, but repeated simulations are computationally expensive, motivating surrogate models for rapid evaluation across geometries and operating conditions. Most existing surrogates are designed for direct field regression, requiring the evaluation of millions of field points even when only an aerodynamic quantity or a localized region is needed, while their internal representations are not intended for direct use in downstream tasks. We introduce AeroJEPA, a framework inspired by joint-embedding predictive architectures that represents the problem in two distinct latent spaces: context tokens encode geometry, while predicted tokens encode the aerodynamic state. Both representations remain directly accessible for downstream tasks, such as linear readouts of design variables and aerodynamic quantities without decoding and integrating the full field. When spatial detail is needed, a continuous implicit decoder evaluates the field only at the requested coordinates while reusing the encoded geometry. We evaluate AeroJEPA on HiLiftAeroML, with multi-million-point fields, and SuperWing, which spans a broad family of transonic wings. Compared with state-of-the-art direct-regression surrogates, AeroJEPA trades peak full-field accuracy for compact, reusable representations. In our selective-decoding experiment, however, AeroJEPA substantially outperforms the evaluated direct-regression surrogates while avoiding predictions over the remainder of the aircraft. The learned representations further support controlled interpolation, concept-vector arithmetic, and preliminary constrained latent-space optimization. These results show how predictive representations can support aerodynamic analysis with or without full-field reconstruction.

Deep generative models and neural operators have demonstrated significant potential for 3D aerodynamic inference. However, they often face inherent challenges in maintaining physical consistency and preserving high-frequency features, primarily due to spectral bias and gradient conflicts within the governing equations. To address these issues, we propose GeoFunFlow-3D, a physics-guided generative flow matching framework. Temporally, we utilize optimal transport theory to build the generation path, ensuring stable training dynamics. Spectrally, we introduce a high-order discrete engine without automatic differentiation (No-AD) to reduce gradient stiffness. Spatially, a topology-aware super-resolution module (SATO) is employed to rigorously enforce physical laws in localized regions such as shock waves. We evaluated our framework on complex industrial datasets. On the BlendedNet dataset, the model successfully avoids mode collapse even under sparse data conditions. For the NASA Rotor37 test, it accurately captures 3D detached shock structures. Compared to conventional operators, GeoFunFlow-3D significantly improves accuracy, reducing the pressure field error (RRMSE) to 0.0215 while maintaining competitive inference efficiency. Ultimately, this work provides a reliable, geometry-driven approach for generating high-dimensional fluid fields.

Deep learning surrogates for CFD flow-field prediction often rely on large, complex models, which can be slow and fragile when data are noisy or incomplete. We introduce FlowForge, a staged local rollout engine that predicts future flow fields by compiling a locality-preserving update schedule and executing it with a shared lightweight local predictor. Rather than producing the next frame in a single global pass, FlowForge rewrites spatial sites stage by stage so that each update conditions only on bounded local context exposed by earlier stages. This compile-execute design aligns inference with short-range physical dependence, keeps latency predictable, and limits error amplification from global mixing. Across PDEBench, CFDBench, and BubbleML, FlowForge matches or improves upon strong baselines in pointwise accuracy, delivers consistently better robustness to noise and missing observations, and maintains stable multi-step rollout behavior while reducing per-step latency.

Data-driven surrogate models can significantly accelerate the simulation of continuous dynamical systems, yet the step-wise accumulation of errors during autoregressive time-stepping often leads to spectral blow-up and unphysical divergence. Existing global regularization techniques can enforce contractive dynamics but uniformly damp high-frequency features, causing over-smoothing; meanwhile, long-horizon trajectory optimization methods are severely constrained by memory bottlenecks. This paper proposes Jacobian-Adaptive Weighting for Stability (JAWS), which reformulates operator learning as a Maximum A Posteriori (MAP) estimation problem with spatially heteroscedastic uncertainty, enabling the regularization strength to adapt automatically based on local physical complexity: enforcing contraction in smooth regions to suppress noise while relaxing constraints near singular features such as shocks to preserve gradient information. Experiments demonstrate that JAWS serves as an effective spectral pre-conditioner for trajectory optimization, allowing short-horizon, memory-efficient training to match the accuracy of long-horizon baselines. Validations on the 1D viscous Burgers' equation and 2D flow past a cylinder ($\text{Re}=400$ out-of-distribution generalization) confirm the method's advantages in long-term stability, preservation of physical conservation properties, and computational efficiency. This significant reduction in memory usage makes the method particularly well-suited for stable and efficient long-term simulation of large-scale flow fields in practical engineering applications.