MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networks

Therefore, it has attracted an increasing amount of attention to combine Physics-informed Neural Networks (PINNs) have machine learning techniques for solving PDEs. Physicsinformed recently achieved remarkable progress in solving Neural Network (PINN) (Raissi et al., 2019) is Partial Differential Equations (PDEs) in various one of the representative approaches that approximate solutions fields by minimizing a weighted sum of PDE loss by training neural networks to minimize a weighted and boundary loss. However, there are several sum of PDE loss and boundary loss -- the former is induced critical challenges in the training of PINNs, including from differential equations while the latter is induced the lack of theoretical frameworks and from boundary and initial conditions. PINN has shown the imbalance between PDE loss and boundary its effectiveness in various sophisticated cases, which has loss. In this paper, we present an analysis of been applied in various fields including fluids mechanics second-order non-homogeneous PDEs, which are (Raissi et al., 2020; Sun et al., 2020), and bio-engineering classified into three categories and applicable to (Sahli Costabal et al., 2020; Kissas et al., 2020).