让神经物理求解器在未知条件下仍保持高精度，突破传统方法局限。
Out-of-Distribution Generalization for Neural Physics Solvers
- 通过学习物理对齐表征，从少量场景中泛化到新参数与几何
- 在非线性问题上误差降低1-2个数量级，显著优于数据驱动基线
- 适合需要探索新假设空间的科学发现与长期动态模拟任务
神经物理求解器在科学发现中日益重要，可快速提供物理、材料或生物系统在仿真中的洞察及其长时间演化。然而，其泛化能力受限于训练数据分布，难以拓展至新设计或长时预测。本文提出NOVA，一种可泛化的神经物理求解器框架，能在偏微分方程参数、几何形状和初始条件发生分布外变化时，仍提供快速且准确的解。通过从初始稀疏场景中学习物理对齐表征，NOVA在复杂非线性问题（如热传导、扩散-反应和流体流动）上，相对于数据驱动基线，实现1-2个数量级的更低分布外误差。进一步展示了其在稳定长时间动力学推演及生成式设计中的双重优势，应用于非线性图灵系统模拟与流体芯片优化。不同于仅限于预设空间内检索或模仿的模型，NOVA实现了对已知范式的可靠外推，满足科学发现中探索新假设空间的核心需求。
原文摘要 · Abstract (English)
Neural physics solvers are increasingly used in scientific discovery, given their potential for rapid in silico insights into physical, materials, or biological systems and their long-time evolution. However, poor generalization beyond their training support limits exploration of novel designs and long-time horizon predictions. We introduce NOVA, a route to generalizable neural physics solvers that can provide rapid, accurate solutions to scenarios even under distributional shifts in partial differential equation parameters, geometries and initial conditions. By learning physics-aligned representations from an initial sparse set of scenarios, NOVA consistently achieves 1-2 orders of magnitude lower out-of-distribution errors than data-driven baselines across complex, nonlinear problems including heat transfer, diffusion-reaction and fluid flow. We further showcase NOVA's dual impact on stabilizing long-time dynamical rollouts and improving generative design through application to the simulation of nonlinear Turing systems and fluidic chip optimization. Unlike neural physics solvers that are constrained to retrieval and/or emulation within an a priori space, NOVA enables reliable extrapolation beyond known regimes, a key capability given the need for exploration of novel hypothesis spaces in scientific discovery
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。