Probabilistic Gradients for Fast Calibration of Differential Equation Models

TL;DR

This paper introduces a probabilistic method for efficiently computing sensitivities in large-scale differential equation models, reducing computational costs and quantifying uncertainty in calibration tasks.

Contribution

It presents a novel probabilistic approach that recycles information and quantifies uncertainty, improving efficiency over classical sensitivity computation methods.

Findings

Reduces computational effort in sensitivity analysis.

Provides probabilistic uncertainty quantification.

Outperforms classical methods in test problems.

Abstract

Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the calculation of local sensitivities, i.e. derivatives of the loss function with respect to the estimated parameters, which often necessitates several numerical solves of the underlying system of partial or ordinary differential equations. In this paper we present a new probabilistic approach to computing local sensitivities. The proposed method has several advantages over classical methods. Firstly, it operates within a constrained computational budget and provides a probabilistic quantification of uncertainty incurred in the sensitivities from this constraint. Secondly, information from previous sensitivity estimates can be recycled in subsequent computations, reducing the overall computational effort for iterative gradient-based calibration methods. The methodology presented is applied to two challenging test problems and compared against classical methods.