Latent Generative Solvers for Generalizable Long-Term Physics Simulation

Reliable physics simulation requires both broad generalization across heterogeneous PDE families and stability under long autoregressive rollouts. Current neural solvers rarely provide both. Deterministic operators accumulate rollout error, while probabilistic solvers typically remain tied to a single PDE family or a short prediction horizon. We address this gap with the \textbf{Latent Generative Solver} (LGS), which couples a Physics VAE (PhyVAE) with a Pyramidal Flow-Forcing Transformer (PFlowFT). PhyVAE compresses states from twelve PDE families into a shared \emph{physical manifold}, separating dynamics-relevant structure from the ambient state space. PFlowFT then predicts the next latent state through input-noised flow matching, yielding a sufficient-condition contraction mechanism that explains improved autoregressive rollout stability. Pretrained on a 2.5\,M-trajectory, 16-system corpus at $128^2$ resolution, LGS obtains the lowest relative $L_2$ error (L2RE) on 15 of 16 systems at both 5- and 10-step rollout. At 20 steps, LGS reduces the L2RE from $56.1\%$ to $\mathbf{30.2\%}$ against matched deterministic and adapted generative baselines, while requiring $\mathbf{13}$--$\mathbf{77\times}$ less recurrent dynamics-step compute. On a held-out $256^2$ Kolmogorov flow, LGS reduces the 1-step L2RE from $0.398$ to $0.129$ within five finetuning epochs; U-AFNO achieves only $0.653$ to $0.343$ under the same protocol.