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Probabilistic gradients for fast calibration of differential equation models

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Title: Probabilistic gradients for fast calibration of differential equation models
Authors: Cockayne, J
Duncan, A
Item Type: Journal Article
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.
Issue Date: 30-Nov-2021
Date of Acceptance: 2-Sep-2021
URI: http://hdl.handle.net/10044/1/92155
DOI: 10.1137/20M1364424
ISSN: 2166-2525
Publisher: Society for Industrial and Applied Mathematics
Journal / Book Title: SIAM/ASA Journal on Uncertainty Quantification
Volume: 9
Issue: 4
Copyright Statement: © 2021 Society for Industrial and Applied Mathematics and American Statistical Association.
Sponsor/Funder: The Alan Turing Institute
Funder's Grant Number: ATI PO 000002890 R/LRF/AD1
Keywords: Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Physics, Mathematical
PDE constrained optimization
sensitivity analysis
probabilistic numerics
0103 Numerical and Computational Mathematics
0104 Statistics
Publication Status: Published
Online Publication Date: 2021-11-30
Appears in Collections:Mathematics
Faculty of Natural Sciences