Discovering governing equations in discrete systems using PINNs

Sparse identification of nonlinear dynamical systems is a topic continuously increasing significance in the community. Here we explore it at level lattice many degrees freedom. We illustrate ability suitable adaptation Physics-Informed Neural Networks (PINNs) to solve inverse problem parameter such discrete, high-dimensional inspired by physical applications. The methodology illustrated diverse array examples including real-field ones (ϕ4 and sine-Gordon), as well complex-field (discrete Schrödinger equation) going beyond Hamiltonian dissipative cases (the discrete complex Ginzburg–Landau equation). Both successes, some limitations method are discussed along way.