Latent Generative Solvers for Generalizable Long-Term Physics Simulation
cs.AI, cs.LG
Submitted: 2026-02-11
Updated: 2026-09-25
License: http://creativecommons.org/licenses/by/4.0/
The gist: Reliable physics simulation demands two capabilities that today's neural PDE solvers do not deliver together: generalization across heterogeneous PDE families, and stability under long autoregressive
Terminology
Abstract
Reliable physics simulation demands two capabilities that today's neural PDE solvers do not deliver together: generalization across heterogeneous PDE families, and stability under long autoregressive rollouts. Deterministic operators accumulate error geometrically, while existing probabilistic solvers are confined to a single PDE family or short horizons. We close this gap with the Latent Generative Solver (LGS), three coupled components: (i) a Physics VAE (PhyVAE) compressing twelve PDE families into a shared latent manifold; (ii) a Pyramidal Flow-Forcing Transformer (PFlowFT) that generates the next latent by flow matching, conditioned on a per-trajectory context updated on the model's own predictions; and (iii) input noising during training, for which we derive a sufficient-condition contraction bound explaining the observed long-horizon stability. Pretrained on a 2.5,M-trajectory, 16-system corpus at 128 squared, LGS matches the strongest deterministic baseline at one step, wins on 15/16 systems at both 5- and 10-step rollout, cuts 20-step L2RE from 56.1% to 30.2%, and uses 13 -- 77 times less recurrent dynamics-step compute. It also adapts efficiently to a 256 squared Kolmogorov flow held out from the pretraining corpus, dropping 1-step L2RE from 0.398 to 0.129 in five finetune epochs against U-AFNO's 0.653 to 0.343. These empirical claims are limited to the evaluated 2D regular-grid systems and discrete horizons.
Sources
- What Regularized Auto-Encoders Learn from the Data Generating Distribution
- Why Exposure Bias Matters: An Imitation Learning Perspective of Error Accumulation in Language Generation
- VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction
- Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion
- FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning
- Auto-Regressive Moving Diffusion Models for Time Series Forecasting
- Ca2-VDM: Efficient Autoregressive Video Diffusion Model with Causal Generation and Cache Sharing
- Towards Multi-spatiotemporal-scale Generalized PDE Modeling
- DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training
- Wavelet Diffusion Neural Operator
- DiffusionPDE: Generative PDE-Solving Under Partial Observation
- Perceiver: General Perception with Iterative Attention
- Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
- Back to Basics: Let Denoising Generative Models Denoise
- Transformer for Partial Differential Equations' Operator Learning
- Fourier Neural Operator for Parametric Partial Differential Equations
- PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers
- PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
- A ConvNet for the 2020s
- SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers
Related papers
- MAVEN-T: Reinforced Heterogeneous Distillation for Real-Time Multi-Agent Trajectory Prediction
- Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world models
- Agents' Last Exam
- The Clinician's Veto: Navigating Trust, Liability, and Uncertainty in Autonomous AI Prescribing
- MindHelper: Closed-Loop Embodied Mental-State Reasoning for Precision Intervention
- Incumbent Advantage: Brand Bias and Cognitive Manipulation Dynamics in LLM Recommendation Systems