Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs

arXiv:2403.10642v1 Announce Type: new
Abstract: Existing work in scientific machine learning (SciML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical partial differential equation (PDE) solvers. Of these, Neural Operators (NOs) have emerged as particularly promising. We observe that several uncertainty quantification (UQ) methods for NOs fail for test inputs that are even moderately out-of-domain (OOD), even when the model approximates the solution well for in-domain tasks. To address this limitation, we …

abstract arxiv cs.lg cs.na data data-driven differential differential equation domain equation machine machine learning math.na numerical observe operators quantification scientific solution type uncertainty work