Discover PDEs using the Adjoint Method

This git repository contains a Python implementation of the adjoint method for discovering PDEs given data. The arxiv version of the corresponding manuscript can be found here: https://doi.org/10.48550/arXiv.2401.17177

Usage

To use this library, import the content of src/ directory via

import sys
import os
src_path = os.path.abspath(os.path.join(os.getcwd(), '../src'))
sys.path.append(src_path)
from adjoint import *

Given that the solution of PDE f discretized on a temporal t and spatial grid x, is stored in a NumPy array with dimension

(number of PDEs, number of time steps, number of grid points in x1, number of grid points in x2, ...)

the adjoint solver can be called simply by

estimated_params, eps, losses = AdjointFindPDE(f, x, dx, data_dt=dt)

For more details, see notebooks in examples/.