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Schmid, N.* ; Fernandes del Pozo, D.* ; Waegeman, W.* ; Hasenauer, J.

Assessment of uncertainty quantification in universal differential equations.

Philos. Trans. R. Soc. A - Math. Phys. Eng. Sci. 383:20240444 (2025)
DOI PMC
Scientific machine learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques to uncover the governing equations of complex processes. Among the available approaches, universal differential equations (UDEs) combine prior knowledge in the form of mechanistic formulations with universal function approximators, such as neural networks. Integral to the efficacy of UDEs is the joint estimation of parameters for both the mechanistic formulations and the universal function approximators using empirical data. However, the robustness and applicability of these resultant models hinge upon the rigorous quantification of uncertainties associated with their parameters and predictive capabilities. In this work, we provide a formalization of uncertainty quantification (UQ) for UDEs and investigate key frequentist and Bayesian methods. By analyzing three synthetic examples of varying complexity, we evaluate the validity and efficiency of ensembles, variational inference and Markov-chain Monte Carlo sampling as epistemic UQ methods for UDEs.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Scientific Machine Learning ; Uncertainty Quantification ; Universal Differential Equations; Systems
ISSN (print) / ISBN 1364-503X
e-ISSN 1471-2962
Zeitschrift Philosophical Transactions of the Royal Society of London, Series A
Quellenangaben Band: 383, Heft: 2293, Seiten: , Artikelnummer: 20240444 Supplement: ,
Verlag Royal Society of London
Verlagsort 6-9 Carlton House Terrace, London Sw1y 5ag, England
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)
Förderungen Bundesministerium für Bildung und Forschung
Vlaamse regering
Rheinische Friedrich-Wilhelms-Universität Bonn
Deutsche Forschungsgemeinschaft
European Research Council