Steven L. Brunton

TL;DR: This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.

TL;DR: In this paper, the authors define dynamic mode decomposition (DMD) as the eigendecomposition of an approximating linear operator, and propose sampling strategies that increase computational efficiency and mitigate the effects of noise.

TL;DR: An overview of machine learning for fluid mechanics can be found in this article, where the strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation.

TL;DR: The intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community and presents a brief overview of several of the well-established techniques.

TL;DR: In this paper, the authors propose a sparse regression method for discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain, which relies on sparsitypromoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models.