Physics Informed Neural Networks as Computational Physics Emulators
This report is a brief overview and evaluation of Physics Informed Neural Networks (PINNs). Karniadakis and co-workers, e.g., Karniadakis et al. (2021) assert that the PINNs approach integrates seamlessly both data and mathematical physics models, even in partially understood, uncertain and high-dimensional contexts. They further claim that PINNs are effective and efficient for ill-posed and inverse problems, and when combined with domain decomposition, are scalable to large problems and a tool to discover hidden physics. While they demonstrate the capabilities in specific academic instances, their overarching claims about PINNs seem to be an overstatement, at least at the current time. We have briefly considered a few of the limitations of PINNs in this investigation. It is not clear to us if the PINNs approach can ever be competitive with approaches that use specialized algorithms to achieve high-accuracy solutions of governing equations and other techniques that can combine observational data with such solutions. As an example of the latter, consistent with the principles of Bayesian inference, data assimilation, or more generally data-model fusion, is a process that fuses observational data typically with a computational model that respects certain constraints such as conservation laws. For example, improvements in observational network combined with data assimilation have been key in improving weather predictions over the past four decades Kalnay (2003).