Recipes for when physics fails: recovering robust learning of physics informed neural networks
Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.
- Research Organization:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Organization:
- National Institutes of Health (NIH); National Science Foundation (NSF); US Army Research Office (ARO); USDOE; USDOE Office of Science (SC), High Energy Physics (HEP)
- Grant/Contract Number:
- SC0007890
- OSTI ID:
- 1923561
- Alternate ID(s):
- OSTI ID: 2419761
OSTI ID: 1909474
- Journal Information:
- Machine Learning: Science and Technology, Journal Name: Machine Learning: Science and Technology Journal Issue: 1 Vol. 4; ISSN 2632-2153
- Publisher:
- IOP PublishingCopyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English