Samuel H. Rudy

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.

TL;DR: In this article, 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.

TL;DR: In this paper, a data-driven method for the discovery of parametric partial differential equations (PDEs) is presented, which allows one to disambiguate between the underlying evolution equations and the underlying PDEs.

TL;DR: In this paper, the authors model the unknown vector field using a deep neural network, imposing a Runge-Kutta integrator structure to isolate this vector field even when the data has a non-uniform timestep, thus constraining and focusing the modeling effort.

TL;DR: In this article, the authors model the unknown vector field using a deep neural network, imposing a Runge-Kutta integrator structure to isolate this vector field even when the data has a non-uniform timestep, thus constraining and focusing the modeling effort.