提出可泛化长期物理模拟的生成式求解器，显著提升稳定性与跨方程适应能力。
Latent Generative Solvers for Generalizable Long-Term Physics Simulation
- 构建共享潜空间的物理变分自编码器，统一建模十二类偏微分方程
- 通过流匹配生成潜变量，实现长达20步的低误差滚动预测（L2RE降至30.2%）
- 训练时引入输入噪声，保障长程稳定，适合需要高效泛化的物理仿真场景
可靠的物理模拟需同时具备跨异构偏微分方程族的泛化能力与长时自回归推演的稳定性。现有神经微分方程求解器或无法跨方程泛化，或仅限短时预测。本文提出隐式生成求解器（Latent Generative Solver, LGS），包含三部分：(i) 物理变分自编码器（PhyVAE）将十二类PDE压缩至共享潜空间；(ii) 分层流驱动变压器（PFlowFT）基于轨迹上下文生成下一时刻潜变量，实现流匹配；(iii) 训练中引入输入噪声，推导出充分条件收缩界，解释长时稳定的成因。在16系统、250万轨迹、128²分辨率的数据集上预训练后，LGS单步精度媲美最强确定性基线，在15/16系统上5步与10步预测表现更优，20步L2RE从56.1%降至30.2%，递归计算量减少13至77倍。对预训练未包含的256²科莫戈罗夫流动，经五次微调，一步L2RE由0.398降至0.129，远优于U-AFNO的0.653→0.343。
原文摘要 · Abstract (English)
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 \textbf{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 $\mathbf{13}$--$\mathbf{77\times}$ 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 $0.653{\to}0.343$.
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