Latent Generative Solvers for Generalizable Long-Term Physics Simulation

arXiv:2602.11229v3 Announce Type: replace 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 extbf{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 128^2, 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 mathbf{30.2%}, and uses mathbf{13}--mathbf{77imes} less recurrent dynamics-step compute. It also adapts efficiently to a 256^2 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{o0.343. These empirical claims are limited to the evaluated 2D regular-grid systems and discrete horizons.

Source: arXiv cs.AI | 2026-09-28

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