Collocation based training of neural ordinary differential equations

Roesch Elisabeth, Rackauckas Christopher and Stumpf Michael P. H. ()
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Roesch Elisabeth: Melbourne Integrative Genomics, University of Melbourne, 30 Royal Parade, Parkville, VIC3052, Australia
Rackauckas Christopher: Department of Mathematics, Massachusetts Institute of Technology, 182 Memorial Dr, Cambridge, MA02142, USA
Stumpf Michael P. H.: Melbourne Integrative Genomics, University of Melbourne, 30 Royal Parade, Parkville, VIC3052, Australia

Statistical Applications in Genetics and Molecular Biology, 2021, vol. 20, issue 2, 37-49

Abstract: The predictive power of machine learning models often exceeds that of mechanistic modeling approaches. However, the interpretability of purely data-driven models, without any mechanistic basis is often complicated, and predictive power by itself can be a poor metric by which we might want to judge different methods. In this work, we focus on the relatively new modeling techniques of neural ordinary differential equations. We discuss how they relate to machine learning and mechanistic models, with the potential to narrow the gulf between these two frameworks: they constitute a class of hybrid model that integrates ideas from data-driven and dynamical systems approaches. Training neural ODEs as representations of dynamical systems data has its own specific demands, and we here propose a collocation scheme as a fast and efficient training strategy. This alleviates the need for costly ODE solvers. We illustrate the advantages that collocation approaches offer, as well as their robustness to qualitative features of a dynamical system, and the quantity and quality of observational data. We focus on systems that exemplify some of the hallmarks of complex dynamical systems encountered in systems biology, and we map out how these methods can be used in the analysis of mathematical models of cellular and physiological processes.

Keywords: collocation; dynamical systems; neural ODE; systems biology (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/sagmb-2020-0025

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