mlsanityData to 14 Oct 2026

Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos

arXiv 2503.18731 ↗First posted 24 Mar 2025cs.LG stat.MLcited by 21

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Autoregressive surrogate models (or textitemulators) of spatiotemporal systems provide an avenue for fast, approximate predictions, with broad applications across science and engineering. At inference time, however, these models are generally unable to provide predictions over long time rollouts due to accumulation of errors leading to diverging trajectories. In essence, emulators operate out of distribution, and controlling the online distribution quickly becomes intractable in large-scale settings. To address this fundamental issue, and focusing on time-stationary systems admitting an invariant measure, we leverage diffusion models to obtain an implicit estimator of the score of this invariant measure. We show that this model of the score function can be used to stabilize autoregressive emulator rollouts by applying on-the-fly denoising during inference, a process we call textitthermalization. Thermalizing an emulator rollout is shown to extend the time horizon of stable predictions by an order of magnitude in complex systems exhibiting turbulent and chaotic behavior, opening up a novel application of diffusion models in the context of neural emulation.

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 34 of its 56 references that are in the map. First posted on arXiv 24 Mar 2025.

Builds on

34 of 56 references.

Closest ancestors · 4

Same direction, newest first

  1. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation4 Sep
  2. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers10 Aug
  3. 2023Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models24 May
  4. 2022Flow Matching for Generative Modeling6 Oct

Other references · 30

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  6. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  7. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  8. 2021Machine learning accelerated computational fluid dynamicscited by 471
  9. 2022Message Passing Neural PDE Solverscited by 386
  10. 2023Neural General Circulation Models for Weather and Climatecited by 239
  11. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  12. 2022FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operatorscited by 188
18 more
  1. 2023GenCast: Diffusion-based ensemble forecasting for medium-range weathercited by 177
  2. 2022Forecasting Global Weather with Graph Neural Networkscited by 168
  3. 2019Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamicscited by 134
  4. 2023Stochastic interpolants with data-dependent couplingscited by 100
  5. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 91
  6. 2021On the difficulty of learning chaotic dynamics with RNNscited by 67
  7. 2023ACE: A fast, skillful learned global atmospheric model for climate predictioncited by 56
  8. 2022Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systemscited by 50
  9. 2022Learning to correct spectral methods for simulating turbulent flowscited by 49
  10. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 49
  11. 2024Statistical optimal transportcited by 47
  12. 2023Training neural operators to preserve invariant measures of chaotic attractorscited by 46
  13. 2023Challenges of learning multi-scale dynamics with AI weather models: Implications for stability and one solutioncited by 31
  14. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 30
  15. 2024LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensemblescited by 30
  16. 2024Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamicscited by 27
  17. 2025Simultaneous emulation and downscaling with physically-consistent deep learning-based regional ocean emulatorscited by 8
  18. 2024Defining error accumulation in ML atmospheric simulatorscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 10; 2026: 11.

21 papers.

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By area:

  1. 2025Panda: A pretrained forecast model for chaotic dynamicscited by 13
  2. 2025Hierarchical Implicit Neural Emulatorscited by 10
  3. 2026Test-time Generalization for Physics through Neural Operator Splittingcited by 10
  4. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  5. 2025Probing forced responses and causality in data-driven climate emulators: conceptual limitations and the role of reduced-order modelscited by 6
  6. 2025Predicting partially observable dynamical systems via diffusion models with a multiscale inference schemecited by 5
  7. 2025Lazy Diffusion: Mitigating spectral collapse in generative diffusion-based stable autoregressive emulation of turbulent flowscited by 4
  8. 2026Can AI Weather Models Predict Beyond Two Weeks? A Quantitative Benchmark and Analysis of Long Rolloutscited by 4
  9. 2025INC: An Indirect Neural Corrector for Auto-Regressive Hybrid PDE Solverscited by 3
  10. 2025Efficient Generative Transformer Operators For Million-Point PDEscited by 2
  11. 2025Generative forecasting with joint probability modelscited by 2
  12. 2026TRIE: An Evaluation Framework for Stochastic PDE Surrogatescited by 2
9 more
  1. 2025Graph-based Neural Space Weather Forecastingcited by 1
  2. 2026Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approachcited by 1
  3. 2026Towards Infinitely Long Neural Simulations: Self-Refining Neural Surrogate Models for Dynamical Systemscited by 1
  4. 2026Deterministic and probabilistic neural surrogates of global hybrid-Vlasov simulationscited by 0
  5. 2026Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilationcited by 0
  6. 2026Eigenanalysis framework for autoregressive neural emulators of multi-scale chaotic dynamicscited by 0
  7. 2026A Constitutive Markov Physics-Informed Neural Operator (MPNO) for Autoregressive Stability in Transient Dynamicscited by 0
  8. 2026Too Rare to Learn: Prescribed Cyclone Tracks Degrade a Bay of Bengal Ocean Emulatorcited by 0
  9. 2026Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave Itcited by 0

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  1. 2026Bias-Constrained Diffusion Schedules for PDE Emulations: Reconstruction Error Minimization and Efficient Unrolled Training
  2. 2026Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems
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