  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 ($\phi^4$ and sine-Gordon), as well as
complex-field (discrete nonlinear Schr{\"o}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.
