A PINN Approach to Symbolic Differential Operator Discovery with Sparse Data

Understand

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators.

• In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data.
• This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics.
• Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition).