物理信息神经网络的梯度手术
Gradient Surgery for Physics-Informed Neural Networks
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中文总结 AI 辅助
本文提出PAM-GS，一种物理感知的梯度手术方法，通过分析PINN训练中的梯度冲突阶段并自适应缓解任务干扰，在多个PDE基准上取得优于现有方法的精度与平衡性能。
中文摘要 AI 辅助
物理信息神经网络（PINNs）通过优化一个将数据拟合与基于物理的约束相结合的组合目标来进行训练，这通常会导致一个高度不平衡的多任务优化问题。在这些条件下，现有的优化策略受到冲突的任务梯度的影响，导致收敛缓慢和训练不稳定，特别是对于刚性和高频偏微分方程。我们分析了使用标准优化器训练PINNs过程中的梯度冲突，并研究了多任务深度学习（MTDL）优化方法。在我们对四个基准问题的分析中，我们观察到PINN优化表现出三个不同的阶段，其中基于角度和基于幅度的梯度冲突交替出现，且每次只出现一种。基于这些观察，我们提出了PAM-GS，一种物理感知的梯度手术方法，它根据观察到的冲突类型在训练过程中自适应地减轻任务干扰。在四个代表性PDE基准上的实验表明，PAM-GS结合了有竞争力的求解精度和持续强大的任务平衡性能，在大多数问题上优于现有方法。
英文摘要
Physics-Informed Neural Networks (PINNs) are trained by optimising a composite objective that combines data fitting with physics-based constraints, typically resulting in a highly imbalanced multi-task optimisation problem. Under these conditions, existing optimisation strategies are affected by conflicting task gradients, leading to slow convergence and unstable training, particularly for stiff and high-frequency partial differential equations. We analyse gradient conflicts throughout training of PINNs with standard optimiser and investigate Multi-Task Deep Learning (MTDL) optimisation methods. In our analysis across four benchmark problems we observed that PINN optimisation exhibits three distinct phases in which angle- and magnitude-based gradient conflicts alternate, with only one present at a time. Building on these observations, we propose PAM-GS, a physics-aware gradient surgery method that adaptively mitigates task interference during training according to the observed conflict types. Experiments on four representative PDE benchmarks demonstrate that PAM-GS combines competitive solution accuracy with consistently strong task-balanced performance, outperforming existing methods on most problems.
发表机构
- Free University of Bozen - Bolzano（博尔扎诺自由大学）
机构由 AI 辅助整理，请以论文原文为准。
