Differential Equations Learning from Spatial-Time Series Data by the Fast Iterative Shrinkage-Thresholding Algorithm

The numerical method of data-driven modeling is presented in this work. It can be used to find the corresponding governing equations in terms of differential equations from some provided spatial and time series data. The problem can be reduced to solve by sparse linear regression technique that can be referred to one of the powerful technique in machine learning algorithm. Here we propose to apply the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and then study the capability of its predictions. The environmental problem involves advection and diffusion effects are demonstrated to show the accuracy and the efficiency for finding all of the coefficients in the partial differential equation corresponding to the input data.