arXiv:2609.03069cs.LG2026-09

通过局部预训练与组合迁移,显著降低物理模拟模型部署成本。

Learnable composition for neural operators

论文配图:Learnable composition for neural operators
图 1 · 摘自论文原文
  • 先在小区域预训练神经算子,再用轻量模块组合局部预测结果。
  • 在大孔隙域上误差比全域模型低36%-56%,仅需16次目标仿真即可适应。
  • 适合需要快速适配新几何或工况的物理仿真场景,如流体与渗流建模。

神经算子是物理仿真的快速可微代理模型,但当域几何、尺寸或运行条件与训练时不同,其精度常下降。监督适配可恢复精度,但即使少量目标数据也需昂贵的高保真仿真。因此我们探讨如何协同设计预训练与迁移以降低部署成本。LatentDDM 先在小子域上预训练神经算子以预测场;针对新场景,冻结该算子,仅训练一个轻量级组合模块来整合局部预测。我们在两个互补问题上评估:稳态达西流中,长程压力耦合需扩展至日益增大的多孔域;非稳态不可压缩流绕俯仰机翼,滚动误差随目标俯仰频率超出训练范围而累积。相比容量相当的全域处理模型,LatentDDM 在适应16次目标仿真后,大达西域误差降低36%-56%。在高速俯仰机翼流动中,20步场滚动预测性能亦提升,无论零样本还是少样本校准均有效。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。

原文摘要 · Abstract (English)

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.

神经算子迁移学习物理模拟少样本

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