Publication Date
2022
Journal or Book Title
arXiv Preprint
Abstract
Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom. We illustrate the ability of a suitable adaptation of Physics-Informed Neural Networks (PINNs) to solve the inverse problem of parameter identification in such discrete, high-dimensional systems inspired by physical applications. The methodology is illustrated in a diverse array of examples including real-field ones (ϕ4 and sine-Gordon), as well as complex-field (discrete nonlinear Schr{ö}dinger equation) and going beyond Hamiltonian to dissipative cases (the discrete complex Ginzburg-Landau equation). Both the successes, as well as some limitations of the method are discussed along the way.
DOI
https://doi.org/10.48550/arXiv.2212.00971
License
UMass Amherst Open Access Policy
Recommended Citation
Saqlain, Sheikh; Zhu, Wei; Charalampidis, Efstathios G.; and Kevrekidis, Panayotis G., "Discovering Governing Equations in Discrete Systems Using PINNs" (2022). arXiv Preprint. 1329.
https://doi.org/10.48550/arXiv.2212.00971