提出混合残差结构提升物理信息神经网络的表达力与可训练性
HyResPINNs: A Hybrid Residual Physics-Informed Neural Network Architecture Designed to Balance Expressiveness and Trainability
- 两层门控结构：基础块内融合光滑基函数与深度网络，整体可门控跳过
- 在多个复杂PDE问题上精度优于基线，训练时间仍具竞争力
- 适合需要高精度物理建模且追求高效训练的研究者
物理信息神经网络（PINNs）通过引入物理约束损失函数来求解偏微分方程（PDE）。本文提出HyResPINNs，一种双层凸门控架构，在固定自由度（DoF）下最大化逼近表达能力。第一层采用可训练组合的光滑基函数与稀疏性控制，并融合深度网络；第二层支持整块门控（类似残差网络或高速网络），实现深度维度上的表达力扩展。在多种挑战性PDE问题上的实证评估表明，HyResPINNs始终在精度上优于基线方法，同时保持相近的训练时间。结果表明，HyResPINNs有望结合传统科学计算与现代机器学习的优势，为物理信息建模提供更鲁棒、更具表现力的新范式。
原文摘要 · Abstract (English)
Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that incorporate physical constraints. In this work, we introduce HyResPINNs, a two-level convex-gated architecture designed to maximize approximation expressiveness for a fixed number of degrees of freedom (DoF). The first level involves a trainable, per-block combination of smooth basis functions with trainable sparsity, and deep neural networks; the second involves the ability to gate entire blocks (much like in ResNets or Highway Nets), allowing for expressivity along the depth dimension of the architecture. Our empirical evaluation on a diverse set of challenging PDE problems demonstrates that HyResPINNs consistently achieve superior accuracy to baseline methods while remaining competitive relative to training times. These results highlight the potential of HyResPINNs to combine desirable features from traditional scientific computing methods and modern machine learning, paving the way for more robust and expressive approaches to physics-informed modeling.
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。