Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks

arXiv:2403.04883v1 Announce Type: cross
Abstract: In this paper, we apply a machine-learning approach to learn traveling solitary waves across various families of partial differential equations (PDEs). Our approach integrates a novel interpretable neural network (NN) architecture, called Separable Gaussian Neural Networks (SGNN) into the framework of Physics-Informed Neural Networks (PINNs). Unlike the traditional PINNs that treat spatial and temporal data as independent inputs, the present method leverages wave characteristics to transform data into the so-called co-traveling wave frame. This adaptation …

abstract apply architecture arxiv cs.lg differential families framework learn machine network networks neural network neural networks novel paper physics physics-informed type