用几何感知神经场预测复杂形状下的稳态偏微分方程，实现高效实时推理。
Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations
- 将几何信息编码为位置锚定的局部特征，保持空间局部性
- 在气动与结构基准上表现优于或媲美现有方法，支持高分辨率网格
- 适合需要快速仿真和复杂形状建模的工程场景
神经算子的进步带来了适用于一般几何的离散化无关代理模型，但许多方法难以高效编码局部几何结构和可变域。我们提出enf2enf，一种用于预测具有几何变化的稳态偏微分方程的神经场方法。该方法将几何信息编码为特定空间位置的潜在特征，全程保持局部性。这些局部表示与全局参数结合后解码为连续物理场，有效建模复杂形状变化。在气动与结构基准上的实验表明，其性能优于或媲美基于图、神经算子及近期神经场方法，支持实时推理并能高效扩展至高分辨率网格。
原文摘要 · Abstract (English)
Advances in neural operators have introduced discretization invariant surrogate models for PDEs on general geometries, yet many approaches struggle to encode local geometric structure and variable domains efficiently. We introduce enf2enf, a neural field approach for predicting steady-state PDEs with geometric variability. Our method encodes geometries into latent features anchored at specific spatial locations, preserving locality throughout the network. These local representations are combined with global parameters and decoded to continuous physical fields, enabling effective modeling of complex shape variations. Experiments on aerodynamic and structural benchmarks demonstrate competitive or superior performance compared to graph-based, neural operator, and recent neural field methods, with real-time inference and efficient scaling to high-resolution meshes.
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。