Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning

arXiv:2404.08809v1 Announce Type: new
Abstract: Uncertainty quantification (UQ) in scientific machine learning (SciML) combines the powerful predictive power of SciML with methods for quantifying the reliability of the learned models. However, two major challenges remain: limited interpretability and expensive training procedures. We provide a new interpretation for UQ problems by establishing a new theoretical connection between some Bayesian inference problems arising in SciML and viscous Hamilton-Jacobi partial differential equations (HJ PDEs). Namely, we show that the posterior mean and covariance …

abstract arxiv challenges cs.lg hamilton however interpretability interpretation machine machine learning major power predictive quantification reliability scientific stat.ml training type uncertainty