Data-driven discovery of free-form governing differential equations

Understand

We present a method of discovering governing differential equations from data without the need to specify a priori the terms to appear in the equation.

• The input to our method is a dataset (or ensemble of datasets) corresponding to a particular solution (or ensemble of particular solutions) of a differential equation.
• The output is a human-readable differential equation with parameters calibrated to the individual particular solutions provided.
• The key to our method is to learn differentiable models of the data that subsequently serve as inputs to a genetic programming algorithm in which graphs specify computation over arbitrary compositions of functions, parameters, and (potentially differential) operators on functions.