Weak-Form Sparse Identification of Nonlinear Dynamics with Applications to Cell Migration
The weak-form sparse identification of nonlinear dynamics (WSINDy) algorithm for inferring nonlinear governing equations from noisy datasets significantly improves the accuracy and robustness to noise of strong-form methods. Furthermore, the weak formulation allows for identification of dynamics from non-classical (weak) solutions. This is accomplished by discretizing a convolutional weak form of the dynamics and using the Fast Fourier Transform to both expedite computations and identify test functions with implicit noise-filtering properties. We will review the nuts and bolts of the WSINDy algorithm and demonstrate its success on several fundamental PDEs including inviscid Burgers, Kuramoto-Sivashinsky, and the Navier-Stokes equations, before diving into new developments relevant to biological equation discovery. In particular, we will discuss the identification of governing equations for particle systems with nonlocal interactions and apply this framework to cellular time series data from wound healing experiments.