Latent Generative Solvers for Generalizable Long-Term Physics Simulation

2026-02-13 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Physics Simulation · Depth: Expert, extended

Summary

Latent Generative Solvers (LGS) is a two-stage framework designed for long-horizon surrogate simulation across diverse Partial Differential Equation (PDE) systems. It employs a pretrained Variational Autoencoder (VAE) to map varied PDE states into a shared latent physics space, followed by a Transformer trained with flow matching to learn probabilistic latent dynamics. A key innovation is an "uncertainty knob" that perturbs latent inputs during training and inference, enabling the solver to correct off-manifold rollout drift and stabilize autoregressive predictions. LGS also uses flow forcing to update a system descriptor (context) from model-generated trajectories, ensuring alignment between training and testing conditions for enhanced long-term stability. Pretrained on a corpus of approximately 2.5 million trajectories at 128^2 resolution across 12 PDE families, LGS achieves comparable short-horizon accuracy to deterministic neural-operator baselines while significantly reducing long-horizon rollout drift. This approach yields up to 70x lower FLOPs than non-generative baselines, facilitating scalable pretraining and efficient adaptation to out-of-distribution 256^2 Kolmogorov flow datasets with limited finetuning.

Key takeaway

For AI Researchers and Scientists developing PDE solvers, LGS offers a robust framework to overcome compounding errors in long-term autoregressive predictions. You should consider integrating latent physics representations and uncertainty-aware generative mechanisms, like the uncertainty knob and flow forcing, to achieve greater stability and generalization across diverse physical systems and resolutions. This approach can significantly reduce computational costs and improve reliability for scientific workflows.

Key insights

LGS uses latent space, generative modeling, and an uncertainty knob for stable, generalizable, and efficient long-term PDE simulation.

Principles

• Decouple spatial representation from temporal modeling.
• Stochasticity stabilizes long-term rollouts by re-entering data manifold.
• Uncertainty-aware models improve long-horizon prediction reliability.

Method

LGS maps PDE states to a latent space via VAE, then learns probabilistic latent dynamics using a Transformer with flow matching, an uncertainty knob, and flow forcing for context updates.

In practice

• Precompute and cache latent trajectories for efficiency.
• Use an uncertainty knob (k) to control off-manifold perturbations.
• Employ temporal pyramids for efficient history conditioning.

Topics

• Latent Generative Solvers
• Neural PDE Solvers
• Physics Simulation
• Flow Matching
• Uncertainty Quantification

Best for: AI Researcher, AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.