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MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networks
Jiachen Yao · Chang Su · Zhongkai Hao · LIU SONGMING · Hang Su · Jun Zhu

Thu Jul 27 01:30 PM -- 03:00 PM (PDT) @ Exhibit Hall 1 #125

Physics-informed Neural Networks (PINNs) have recently achieved remarkable progress in solving Partial Differential Equations (PDEs) in various fields by minimizing a weighted sum of PDE loss and boundary loss. However, there are several critical challenges in the training of PINNs, including the lack of theoretical frameworks and the imbalance between PDE loss and boundary loss. In this paper, we present an analysis of second-order non-homogeneous PDEs, which are classified into three categories and applicable to various common problems. We also characterize the connections between the training loss and actual error, guaranteeing convergence under mild conditions. The theoretical analysis inspires us to further propose MultiAdam, a scale-invariant optimizer that leverages gradient momentum to parameter-wisely balance the loss terms. Extensive experiment results on multiple problems from different physical domains demonstrate that our MultiAdam solver can improve the predictive accuracy by 1-2 orders of magnitude compared with strong baselines.

Author Information

Jiachen Yao (Tsinghua University)
Chang Su (Tsinghua University)
Zhongkai Hao (Tsinghua University)
LIU SONGMING (Tsinghua University)
Hang Su (Tsinghua University)
Jun Zhu (Tsinghua University)

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