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Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks.
- Source :
- Entropy; May2024, Vol. 26 Issue 5, p396, 19p
- Publication Year :
- 2024
-
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, b-family of PDEs. In addition, we expand our investigations, and explore not only peakon solutions in the a b -family but also compacton solutions in (2+1)-dimensional, Rosenau-Hyman family of PDEs. A comparative analysis with multi-layer perceptron (MLP) reveals that SGNN achieves comparable accuracy with fewer than a tenth of the neurons, underscoring its efficiency and potential for broader application in solving complex nonlinear PDEs. [ABSTRACT FROM AUTHOR]
- Subjects :
- PARTIAL differential equations
MACHINE learning
Subjects
Details
- Language :
- English
- ISSN :
- 10994300
- Volume :
- 26
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Entropy
- Publication Type :
- Academic Journal
- Accession number :
- 177488154
- Full Text :
- https://doi.org/10.3390/e26050396