Training of physics-informed neural networks: a multi-criterion viewpoint

Partial differential equations (PDEs) are usually solved by numerical methods requiring specific grids and discretisation schemes. Physics-Informed Neural Networks (PINNs) have emerged recently, as a more flexible alternative approach. They are based on feed-forward neural networks, whose parameters are calibrated by minimisation of a loss function combining the residuals of the PDEs, the boundary conditions and possible data.