## Data Driven Governing Equations Recovery with Deep Neural Networks

**
Dongbin Xiu **

Department of Mathematics

The Ohio State University

We present effective numerical algorithms for recovering unknown governing equations
from measurement data. Upon recasting the problem into a function approximation
problem, we discuss the importance of using a large number of short bursts of trajectory
data, rather than using data from a small number of long trajectories. Several recovery
strategies using deep neural networks (DNNs) are presented. We demonstrate that
residual network (ResNet) is particularly suitable for equation discovery, as it can produce
exact time integrator for numerical prediction. We then present a set of applications of the
DNN learning of unknown dynamical systems, which may contain random parameters or
missing variables, as well as learning of unknown partial differential equations. The
numerical examples demonstrate that DNNs can be a highly effective tool for data driven
physics recovery.