ArticleEntropy (Basel, Switzerland)2024
Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks.
Article in Entropy (Basel, Switzerland), 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
In this paper, we apply a machine-learning approach to learn traveling solitary waves across various physical systems that are described by 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 reformulation effectively addresses the issue of propagation failure in PINNs when applied to large computational domains. Here, the SGNN architecture demonstrates robust approximation capabilities for single-peakon, multi-peakon, and stationary solutions (known as "leftons") within the (1+1)-dimensional,
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