Journal
INTERNATIONAL STATISTICAL REVIEW
Volume 91, Issue 3, Pages 464-492Publisher
WILEY
DOI: 10.1111/insr.12554
Keywords
differential equations; dynamic equation discovery; probabilistic dynamic equation discovery
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This paper reviews the current literature on data-driven discovery for dynamic systems, providing a categorization and unified mathematical framework for different approaches. It discusses the role of statistics in the field and presents avenues for future work.
Many real-world scientific processes are governed by complex non-linear dynamic systems that can be represented by differential equations. Recently, there has been an increased interest in learning, or discovering, the forms of the equations driving these complex non-linear dynamic systems using data-driven approaches. In this paper, we review the current literature on data-driven discovery for dynamic systems. We provide a categorisation to the different approaches for data-driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data-driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework and provide avenues for future work.
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