mlsanityData to 14 Oct 2026

Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics

arXiv 2610.04108 ↗First posted 2 Oct 2026cs.LG nlin.CDcited by 0

Not on the map. Why?

Abstract (arXiv)

Accelerating the prediction of long-term behavior in chaotic systems is crucial in scientific computing. However, existing methods rely on numerical solvers or autoregressive models that advance one small step at a time, which makes long horizons expensive. We instead view this problem as learning the system's time-invariant evolution operator, which jumps the state across a large time span in a single evaluation. To this end, we derive the consistency equations a time-invariant operator must satisfy, with differential and compositional objectives in physical time. These equations also connect the learned operator to the physics-prescribed instant dynamics, enabling physics embedding in consistency learning. Across five chaotic systems, we find that physics-distilled consistency makes both short-term trajectories and long-term statistics more accurate. The learned operator survives temporal extrapolation and requires one-tenth as many evaluations as autoregressive rollout, offering an efficient route to long-term simulation of chaotic dynamics.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 28 of its 52 references that are in the map. First posted on arXiv 2 Oct 2026.

Builds on

28 of 52 references.

References · 28

  1. 2022Scalable Diffusion Models with Transformerscited by 6,054
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  4. 2023Consistency Modelscited by 1,822
  5. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  6. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  7. 2025Mean Flows for One-step Generative Modelingcited by 561
  8. 2021Machine learning accelerated computational fluid dynamicscited by 471
  9. 2024One Step Diffusion via Shortcut Modelscited by 391
  10. 2022Message Passing Neural PDE Solverscited by 386
  11. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 109
  12. 2025How to build a consistency model: Learning flow maps via self-distillationcited by 103
16 more
  1. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 96
  2. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 88
  3. 2021On the difficulty of learning chaotic dynamics with RNNscited by 67
  4. 2023Generalized Teacher Forcing for Learning Chaotic Dynamicscited by 58
  5. 2019Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRIcited by 41
  6. 2025Transition Models: Rethinking the Generative Learning Objectivecited by 34
  7. 2024Zero-shot forecasting of chaotic systemscited by 28
  8. 2025Terminal Velocity Matchingcited by 20
  9. 2022Open Source Vizier: Distributed Infrastructure and API for Reliable and Flexible Blackbox Optimizationcited by 18
  10. 2025Recurrent Neural Operators: Stable Long-Term PDE Predictioncited by 16
  11. 2023Deep-OSG: Deep Learning of Operators in Semigroupcited by 11
  12. 2025CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operatorscited by 11
  13. 2026Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamicscited by 7
  14. 2026Semigroup Consistency as a Diagnostic for Learned Physics Simulatorscited by 4
  15. 2026Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistencycited by 1
  16. 2026Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlowcited by 1

Built on by

Not cited yet.