让神经网络学会通用求解微分方程，能适应从未见过的新方程。
Generalizing PDE Emulation with Equation-Aware Neural Operators
- 用方程项和系数的向量编码来指导神经网络，实现方程感知建模。
- 在未见参数和新方程上表现稳定，长时滚动预测误差小。
- 适合需要快速泛化求解复杂微分方程的研究者或工程应用。
传统数值方法求解偏微分方程（PDE）成本高昂。基于深度学习的代理模型通常仅针对单一固定参数的PDE。本文提出一种方程感知的泛化模拟框架，将神经模型条件于编码了方程各项及其系数的向量。我们基于APEBench套件中的1D PDE家族，构建了四种不同建模范式。该方法在训练分布外的参数设置上表现优异，长时滚动预测保持稳定，并成功泛化至完全未见过的PDE。本工作是探索由AI自动构建可评分科学任务专家级软件系统的一部分。数据与代码已开源：https://github.com/google-research/generalized-pde-emulator。
原文摘要 · Abstract (English)
Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for equation-aware emulation that generalizes to unseen PDEs, conditioning a neural model on a vector encoding representing the terms in a PDE and their coefficients. We present a baseline of four distinct modeling technqiues, trained on a family of 1D PDEs from the APEBench suite. Our approach achieves strong performance on parameter sets held out from the training distribution, with strong stability for rollout beyond the training window, and generalization to an entirely unseen PDE. This work was developed as part of a broader effort exploring AI systems that automate the creation of expert-level empirical software for scorable scientific tasks. The data and codebase are available at https://github.com/google-research/generalized-pde-emulator.
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。