Uncertainty Quantification in Neural Differential Equations

Abstract

Uncertainty quantification (UQ) helps to make trustworthy predictions based on collected observations and uncertain domain knowledge. With increased usage of deep learning in various applications, the need for efficient UQ methods that can make deep models more reliable has increased as well. Among applications that can benefit from effective handling of uncertainty are the deep learning based differential equation (DE) solvers. We adapt several state-of-the-art UQ methods to get the predictive uncertainty for DE solutions and show the results on four different DE types.

Cosmology-informed neural networks to solve the background dynamics of the Universe

“…( 31), but with the difference that z is not fixed at z 0 . 9 A recent work [53] showed how to estimate uncertainties in the general framework. The application to the cosmological context is left for future work.…”