Someone has already mentioned Neural Ordinary Differential Equations, which is also the first thing that came to mind. There are also extensions to it, where one can use PDEs(Neural Hamiltonian Flows) or even stochastic DEs(Score-Based Generative Models) in the model. All of them covering different but overlapping use cases.

There are also techniques which use numerical solvers as blackboxes to perform model-order reduction of a complicated system of equations, or identifying slow modes, timescale decomposition, etc.