Published: Aug. 30, 2021
Dan Messenger, Department of Applied Mathematics, University of Colorado Boulder

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.ÌýThis is accomplished by discretizing a convolutional weak form of the dynamics and using the Fast Fourier Transform to both expedite computations and identify testÌýfunctions with implicit noise-filtering properties. We will review the nuts and bolts of the WSINDy algorithm and demonstrate itsÌýsuccess on several fundamental PDEs including inviscid Burgers, Kuramoto-Sivashinsky, and the Navier-Stokes equations, before diving into new developments relevant to biological equation discovery.ÌýIn particular, we will discuss the identification of governingÌýequations for particle systems with nonlocalÌýinteractions and apply this framework to cellular time series data from wound healing experiments.

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