LIGO-PINN：通过门控优化进行学习初始化以缓解物理信息神经网络中的收敛失败
LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks
- Stevens Institute of Technology（史蒂文斯理工学院）
- Wageningen University & Research（瓦赫宁根大学及研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究针对物理信息神经网络（PINNs）收敛失败问题，提出通过门控逐层优化进行学习初始化的框架LIGO-PINN。经多领域严格评估，该方法性能优于现有方法，能有效缓解收敛失败，还可推广到3D非结构化领域，并分析了训练动态。
AI中文摘要：
物理信息神经网络（PINNs）在由偏微分方程（PDE）控制的建模领域产生了广泛的研究影响。然而，在具有挑战性的PDE领域，或推广到未见但相关的PDE领域时，PINNs表现不佳，有时甚至收敛到平凡解。先前提出的解决方案包括超参数调整、基于课程学习的训练策略或硬配置点的动态重采样，但都存在一定缺陷。我们认为PINN网络权重初始化在训练灾难性失败中起关键作用，却未被充分研究。为此，我们提出了通过门控逐层优化进行学习初始化的框架（LIGO-PINN）来克服PINN收敛失败。通过在1D和2D PDE领域的严格评估，包括具有挑战性的2D流体动力学设置，我们证明我们的方法优于旨在缓解PINN失败的现有方法，在六个基线中平均性能提高了91.5%，比最强基线提高了81%。我们还验证了LIGO-PINN可推广到3D非结构化领域。最后，我们分析了所有三个PDE领域的训练动态，以解释LIGO-PINN方法的改进和传统PINNs的收敛失败。
英文摘要：
Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE). However, PINNs have been shown to perform poorly, sometimes even converging to trivial solutions, in challenging PDE domains, or when generalizing to unseen but related PDE domains. Previously proposed solutions detail hyperparameter tuning to reduce loss imbalance between data-driven and physics guided losses, curriculum learning based training strategies, or dynamic re-sampling of hard collocation points. These methods face certain pitfalls: hyperparameter tuning is expensive, designing a training curriculum is ambiguous in multi-parameter PDE settings, and dynamic resampling still fails in complex PDE settings. Complementary to this line of thinking, we believe the initial PINN network weights also play a crucial role in the emergence of catastrophic failures during training, yet the effect of PINN weight initialization has been surprisingly under-investigated. To this end, we propose a framework for Learned Initialization via Gated Layerwise Optimization (LIGO-PINN) to overcome PINN convergence failures. Through rigorous evaluation on 1D and 2D PDE domains, including a challenging 2D fluid dynamics setting, we demonstrate that our methodology outperforms state-of-the-art methods designed to alleviate PINN failures, achieving a 91.5% average performance improvement across six baselines and 81% over the strongest baseline. We also verify that LIGO-PINN generalizes to 3D unstructured domains. Finally, we analyze training dynamics across all three PDE domains to explain both LIGO-PINN's improvement and the convergence failure of traditional PINNs. Code: https://github.com/scailab/ligo-pinn Keywords: Machine Learning, Physics-Informed Neural Networks, Deep Learning, PDE Modeling
