Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics

Understand

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data.

• In many instances, such models are in the form of nonlinear partial differential equations (PDEs); hence sparse regression typically requires evaluation of various partial derivatives.
• However, accurate evaluation of derivatives, especially of high order, is infeasible when the data are noisy, which has a dramatic negative effect on the result of regression.
• We present a novel and rather general approach that addresses this difficulty by using a weak formulation of the problem.