发表机构
MIT MechE; University of Toronto（麻省理工学院机械工程系; 多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出LatentDDM方法，通过预训练神经算子并训练轻量组合模块，在达西流和翼型流任务上降低了误差，为物理基础模型提供了新设计原则。
AI 中文摘要
神经算子是物理模拟的快速可微替代模型，但当域几何、大小或运行条件与训练集不同时，其精度常下降。监督式自适应可恢复精度，但即使少量目标集也需要高成本的高保真模拟。因此，本文探究如何协同设计预训练与迁移以降低部署成本：LatentDDM首先预训练一个神经算子，用于预测小子域上的场；对于新场景，该方法冻结此算子，仅训练一个轻量模块来组合局部预测。我们在两个互补问题上评估该方法：一是稳态达西流，其中长程压力耦合需延伸至越来越大的多孔域；二是俯仰翼型周围的非稳态不可压缩流，其中当目标俯仰频率超出训练范围时，滚动误差会累积。与一次性处理全域的容量匹配模型相比，在使用16个目标模拟进行自适应后，LatentDDM在更大达西域上的误差降低了36%-56%；同时，在快俯仰翼型流的20步场滚动中，无论是零样本还是少样本校准后，其性能均有所提升。这些结果表明，协同设计的局部预训练与组合级迁移是物理基础模型的有前景设计原则。
英文摘要
Neural operators are fast, differentiable surrogates for physical simulation, but their accuracy often degrades when domain geometry, size, or operating conditions differ from training. Supervised adaptation can recover accuracy, but even a small target set requires costly high-fidelity simulations. We therefore ask how pretraining and transfer can be designed together to reduce this deployment cost. LatentDDM first pretrains a neural operator to predict fields on small subdomains. For a new setting, it freezes this operator and trains only a lightweight module that composes the local predictions. We evaluate our method on two complementary problems: steady Darcy flow, where long-range pressure coupling must extend across increasingly large porous domains, and unsteady incompressible flow around a pitching airfoil, where rollout errors compound as target pitching frequencies exceed the training range. Compared with the capacity-matched models that process the full domain at once, LatentDDM's error is 36-56% lower on larger Darcy domains after adaptation with 16 target simulations. It also improves 20-step field rollouts in fast-pitching airfoil flow, both zero-shot and after few-shot calibration. These results identify the co-designed local pretraining and composition-level transfer as a promising design principle for physical foundation models.
