Governing equations are essential to the study of physical systems, providing models that can generalize to predict previously unseen behaviors. There are many systems of interest across disciplines where large quantities of data have been collected, but the underlying governing equations remain unknown. This work introduces an approach to discover governing models from data. The proposed method addresses a key limitation of prior approaches by simultaneously discovering coordinates that admit a parsimonious dynamical model. Developing parsimonious and interpretable governing models has the potential to transform our understanding of complex systems, including in neuroscience, biology, and climate science.
Data-driven discovery of coordinates and governing equations
Kathleen Champion, Bethany Lusch, J. Nathan Kutz, and Steven L. Brunton
PNAS November 5, 2019 116 (45) 22445-22451; first published October 21, 2019 https://doi.org/10.1073/pnas.1906995116