Differentiable composition for model discovery

We propose DiffComp, a symbolic regressor that can learn arbitrary function compositions, including derivatives of various orders. We use DiffComp in conjunction with a Physics Informed Neural Network (PINN) to discover differential equations from data. DiffComp has a layered structure where a set of user-defined basic functions are composed up to a specified depth. As it is differentiable, it can be trained using gradient descent. We test the architecture using simulated data from common PDEs and compare to existing model discovery frameworks, including PySINDy and DeePyMoD. We then test on oceanographic data.