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Maddu, S.* ; Cheeseman, B.L.* ; Müller, C. ; Sbalzarini, I.F.*

Learning physically consistent differential equation models from data using group sparsity.

Phys. Rev. E 103:042310 (2021)
Publ. Version/Full Text DOI
Open Access Gold (Paid Option)
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We propose a statistical learning framework based on group-sparse regression that can be used to (i) enforce conservation laws, (ii) ensure model equivalence, and (iii) guarantee symmetries when learning or inferring differential-equation models from data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas such as biology, high noise levels, sensor-induced correlations, and strong intersystem variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn biologically plausible and physically consistent models rather than models that simply fit the data best. We present the group iterative hard thresholding algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Nonlinear Dynamics; Pattern-formation; Identification; Systems; Optimization; Pursuit; Tissue; Sensor
ISSN (print) / ISBN 1063-651X
e-ISSN 1550-2376
Quellenangaben Volume: 103, Issue: 4, Pages: , Article Number: 042310 Supplement: ,
Publisher American Physical Society (APS)
Publishing Place Melville, NY
Reviewing status Peer reviewed
Grants Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI Dresden/Leipzig - Federal Ministry of Education and Research (Bundesministerium fur Bildung und Forschung)
German Research Foundation (Deutsche Forschungsgemeinschaft) under Germany's Excellence Strategy, Cluster of Excellence "Physics of Life" of TU Dresden