Lagrangian PINNs: A causality-conforming solution to failure modes of physics-informed neural networks. (arXiv:2205.02902v1 [cs.LG])

Web: http://arxiv.org/abs/2205.02902

Physics-informed neural networks (PINNs) leverage neural-networks to find the
solutions of partial differential equation (PDE)-constrained optimization
problems with initial conditions and boundary conditions as soft constraints.
These soft constraints are often considered to be the sources of the complexity
in the training phase of PINNs. Here, we demonstrate that the challenge of
training (i) persists even when the boundary conditions are strictly enforced,
and (ii) is closely related to the Kolmogorov n-width associated with problems
demonstrating transport, convection, traveling waves, …

arxiv causality failure networks neural neural networks physics