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3 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Jul 6Week of Sep 21

Latest papers 16

Sep 20, 2026cs.LG

The Neural Forcing for Three-Dimensional Incompressible Navier-Stokes finite time blowup

We present a two-part neural framework for forced three-dimensional incompressible Navier--Stokes flow. PartI develops the computational forcing system. A physics-informed neural model generates structured external-force trajectories, candidates are optimized through differentiable PDE rollouts or PPO-Clip, and selected forcings are frozen and checked by independent fixed-force replay. PartII provides the mathematical certification layer. It separates neural candidate discovery from continuum analysis, derives integrated reciprocal-vorticity criteria that imply Riccati-type growth and finite-time loss of smooth continuation, develops a validated computational-to-continuum transfer strategy, and establishes a conditional positive-probability closure for a nondegenerate neural output law. The proof is complete at the continuum level.

Beibei Li

Reynolds-Averaged Navier-Stokes Vortex Neural Ordinary Differential Equations Single Trajectory

Sep 14, 2026physics.flu-dyn

Computer-assisted global regularity across nonlinear families of three-dimensional periodic Navier-Stokes flows

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.

Jose Luis Lima de Jesus Silva

Federal University of Bahia, Department of Geophysics Salvador, BA 40170-115, Brazil · Grupo de Estudos e Aplicação de Inteligência2026 Artificial em Geofísica (GAIA) Federal University of Bahia, Salvador, BA 40170-115, Brazil

Vortex Reynolds-Averaged Navier-Stokes Regularity Nonlinearity

Sep 1, 2026cs.LG

VATO: A Vortex-Force-Aware Transformer Operator for Unsteady Separated Aerofoil 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.

Xingxin Yang, Zhan Zhang, Yichen Li +1

aDepartment of Engineering, King’s College London, London, WC2R 2LS, UK

Vortex Aerodynamics

Aug 1, 2026cs.LG

Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers

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.

Farbod Faraji, Francesco Belardinelli

Department of Computing, Huxley Building, Imperial College London 180 Queen’s Gate, South Kensington, London SW7 2RH, United Kingdom

Vortex Dynamical Systems Nonlinear Dynamics Model Discovery Neuro-Symbolic Framework Generative Pretrained Transformers

Aug 1, 2026stat.ML

Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errors

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.

Alexander Scheinker

Los Alamos National Laboratory Los Alamos, NM, 87544, USA

Diffusion Models Vortex

Jul 22, 2026physics.flu-dyn

Guarantees by Construction for Learned Finite Volume Schemes on Steady Supersonic Flow

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.

Denis Gueyffier

ONERA -- Institut Polytechnique de Paris · Direction Scientifique G´en´erale, ONERA · Institut Polytechnique de Paris, Palaiseau, France

Vortex Turbulent Flows Fundamental Limits Construction

Jul 15, 2026cs.RO

Flow-aware Optimal Navigation in Unsteady Flows through Reinforcement Learning

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.

Andrea Maria Braghin, Nicolò Botteghi, Matteo Tomasetto +2

Department of Mechanical Engineering, Politecnico di Milano, Milano, Italy · MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy

Robot Navigation Reinforcement Learning Control Vortex Robust Trajectory Navigation

Jun 23, 2026cs.CE

Neural Network-Based Parametric Model Reduction for Predicting Turbulent Flow for Different Vehicle Geometries

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.

Kazuto Ando, Rahul Bale, Akiyoshi Kuroda +1

Operations and Computer Technologies Division, RIKEN Center for Computational Science 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan · Complex Phenomena Unified Simulation Research Team, RIKEN Center for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan · Department of Computational Science, Graduate School of System Informatics, Kobe University, 1-1, Rokkodai-cho, Nada-ku, Kobe, 657-8501, Hyogo, Japan

Reduced-Order Models Vortex Aerodynamics Queryable Sector Flow Fields

Jun 18, 2026cs.CV

Vortex: Multi-Modal Fusion System for Intelligent Video Retrieval

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.

Duc-Tho Nguyen, Hieu-Hoc Tran-Minh, Khanh-Hoa Lam +4

University of Science, VNU-HCM, Ho Chi Minh City, Vietnam · Vietnam National University, Ho Chi Minh City, Vietnam

Multimodal Retrieval Multimodal Fusion Vortex

Jun 9, 2026cs.MA

Multi-agent rendezvous in fluid flows via reinforcement learning

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.

Bocheng Li, Jingran Qiu, Lihao Zhao

11AML, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084 China. · Department of Physics, Gothenburg University, Gothenburg, 41296 Sweden.

Multi-Agent Reinforcement Learning Vortex Fluid Dynamics Swarms

Jun 4, 2026cs.AI

Vortex: Efficient and Programmable Sparse Attention Serving for AI Agents

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.

Zhuoming Chen, Xinrui Zhong, Qilong Feng +5

1Carnegie Mellon University · 2Rice University · 3National University of Singapore

Dynamic Sparse Attention Large Language Model Serving Artificial Intelligence Agents Vortex

May 28, 2026cs.LG

Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor

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.

Minseo Lee, Seongmin Oh, Chaehyeon Song +5

Division of Advanced Nuclear Engineering, POSTECH, 772026 Cheongam-Ro, Pohang-si, 37673, Gyeongbuk-do, Republic of Korea · Department of Quantum System Engineering, Jeonbuk National University, 567 Baekje-daero, Jeonju-si, 54896, Jeollabuk-do, Republic of Korea · Department of Nuclear Engineering, Hanyang University, Wangsimni-ro, Seongdong-gu, Seongdong-gu, 04763, Seoul, Republic of Korea +1

Computational Fluid Dynamic Surrogate Models Nuclear Fusion Vortex

May 23, 2026cs.LG

WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations

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.

Muhammad Abid, Arth Sojitra, Omer San

Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville Knoxville, TN 37996, USA.

Fourier Neural Operators Partial Differential Equations Neural Operators Wavelets Vortex

May 8, 2026cs.LG

A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots

The population dynamics of molecules, cells, and organisms are governed by a number of unknown forces. In the last decade, population dynamics have predominantly been modeled with Wasserstein gradient flows. However, since gradient flows minimize free energy, they fail to capture important dynamical properties, such as periodicity. In this work, we propose a change in perspective by considering dynamics that minimize a population-level action under a damped Wasserstein Lagrangian. By deriving the corresponding Hamiltonian equations of motion, we formalize Wasserstein Lagrangian Mechanics, a structured class of second-order dynamics that encompasses classical mechanics, quantum mechanics, and gradient flows. We then propose WLM as the first algorithm that learns these second-order dynamics from observed marginals, without specifying the Lagrangian. By directly learning the population mechanics, WLM can both forecast and interpolate unseen marginals, and outperforms existing gradient flow and flow matching methods across a wide range of dynamics, including vortex dynamics, embryonic development, and flocking.

Vincent Guan, Lazar Atanackovic, Kirill Neklyudov

University of British Columbia · Mila - Quebec AI Institute · University of Alberta +4

Lagrangian Methods Population Dynamics Wasserstein Distance Vortex Gradient Snapshots+1

Apr 22, 2026cs.LG

On the Role of Strain and Vorticity in Numerical Integration Error for Flow Matching

Flow matching generates data by integrating a learned velocity field, where the number of integration steps (NFE) directly determines inference cost. We analyze which properties of the velocity field govern integration error by decomposing the velocity Jacobian into its symmetric part S (strain rate) and antisymmetric part Omega (vorticity). We prove that strain and vorticity play different roles: strain controls exponential error amplification through the logarithmic norm, while vorticity contributes only linearly to the local truncation error. We further show that the optimal transport velocity field is irrotational and has zero material derivative, implying second-order Euler accuracy; for exact displacement interpolation, the associated Lagrangian particle dynamics are integrated exactly by Euler. Motivated by this analysis, we study weighted Jacobian regularization with strain weight alpha and vorticity weight beta. Experiments on 2D synthetic data confirm the main theoretical predictions, showing up to 2.7x lower integration error at NFE=5. Preliminary CIFAR-10 experiments show consistent trends, with a lightweight fine-tuning procedure improving FID by 14 percent at NFE=10 while preserving high-NFE quality.

Chenxi Tao, Seung-Kyum Choi

Georgia Institute of Technology

Vortex Time Discretization Jacobian

Jul 1, 2025physics.flu-dyn

Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence

Typically, numerical simulations of Earth systems are coarse, and Earth observations are sparse and gappy. We apply four generative diffusion modeling approaches to super-resolution and inference of forced two-dimensional quasi-geostrophic turbulence on the beta-plane from coarse, sparse, and gappy observations. Two guided approaches minimally adapt a pre-trained unconditional model: SDEdit modifies the initial condition, and Diffusion Posterior Sampling (DPS) modifies the reverse diffusion process score. Two conditional approaches, a vanilla variant and classifier-free guidance, require training with paired high-resolution and observation data. We consider multiple test cases spanning: two regimes, eddy and anisotropic-jet turbulence; two Reynolds numbers, 10^3 and 10^4; and two observation types, 4x coarse-resolution fields and coarse, sparse and gappy observations. Our comprehensive skill metrics include norms of the reconstructed vorticity fields, turbulence statistical quantities, and quantifications of the super-resolved probabilistic ensembles and their errors. We also study the sensitivity to tuning parameters such as guidance strength. Results show that the generated super-resolution fields of SDEdit are unphysical, while those of DPS are reasonable but with smoothed fine-scale features; however, neither of these lower-cost models propagates observational information effectively to unobserved regions. The two conditional models require re-training, but reconstruct missing fine-scale features, are cycle-consistent with observations, and predict correct turbulence statistics, including the tails. Further, their mean errors are highly correlated with and predictable from their ensemble standard deviations. Results highlight the tradeoffs between ease of implementation, fidelity (sharpness), and cycle-consistency of the diffusion models, and offer practical guidance for deployment.

Anantha Narayanan Suresh Babu, Akhil Sadam, Pierre F. J. Lermusiaux

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA · Center for Computational Science and Engineering, Massachusetts Institute of Technology, Cambridge, USA

Turbulent Flows Generative Super-Resolution Diffusion Sampling Generative Models Vortex Earth Observation+1