Data driven discovery of sparse dynamics

Rachel Ward and collaborator Giang Tran (former Bing Instructor in the UT Mathematics department) are investigating the identification of a dynamical system (say, within the class of polynomial systems of ordinary differential equations) given snapshots of the system in time. Such problems prove challenging when there is a high level of noise on the data. In the paper Exact recovery of Chaotic systems from highly corrupted data, they show that if the underlying trajectory exhibits ergodicy or chaos, and if the underlying dynamics have a sparse representation with respect to the polynomial basis, then a LASSO / l1 type algorithm will exactly recover the underlying dynamics even when most of the data is highly corrupted. This establishes a new link between the areas of dynamical systems and machine learning / sparse recovery, and many interesting questions remain.