Uncertainty Quantification in Neural Differential Equations

TL;DR

This paper explores the adaptation of advanced uncertainty quantification methods to neural differential equations, enhancing the reliability of deep learning-based DE solvers across various types.

Contribution

It introduces the application of multiple state-of-the-art UQ techniques to neural DE solvers, demonstrating their effectiveness in quantifying predictive uncertainty.

Findings

UQ methods successfully quantify uncertainty in neural DE solutions

Improved reliability of deep learning-based DE solvers demonstrated

Applicability across four different types of 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.