Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUp

arXiv:2310.05169v2 Announce Type: replace
Abstract: Physics Informed Neural Networks (PINNs) have been achieving ever newer feats of solving complicated PDEs numerically while offering an attractive trade-off between accuracy and speed of inference. A particularly challenging aspect of PDEs is that there exist simple PDEs which can evolve into singular solutions in finite time starting from smooth initial conditions. In recent times some striking experiments have suggested that PINNs might be good at even detecting such finite-time blow-ups. In this work, …

abstract accuracy arxiv cs.lg cs.na inference math.ap math.na near networks neural networks physics simple solve speed trade trade-off type