Data-Driven Discovery of Governing Equations

Abstract

Theoretical equations are the basis of scientific progress. Many scientific domains still lack the appropriate theoretical model to reason about the phenomena. With the rise of data, there is an increasing need for methodology in data-driven science and engineering for understanding the physical phenomena. This thesis on Data-Driven Discovery of Governing Equations aims to provide a method for model discovery and find governing partial differential equations from data by training physics-informed neural networks. Given data, our method generalizes a neural network to compute a matrix of candidate terms for Partial Differential Equation(PDE). Minimizing the residuals from the candidate matrix allows us to find the coefficients for the governing equation. We present a framework to discover PDE not restricted to first-order time derivative equations.