Learning differentiable solvers for systems with hard constraints

Understand

We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance.

• We develop a differentiable PDE-constrained layer that can be incorporated into any NN architecture.
• Our method leverages differentiable optimization and the implicit function theorem to effectively enforce physical constraints.
• Inspired by dictionary learning, our model learns a family of functions, each of which defines a mapping from PDE parameters to PDE solutions.