PDE Estimation

The code in this repository describes the procedure for estimating the form of a PDE that generates a set of data.

To run a parameter estimation, choose a PDE and run python3 run_inv.py $EQN where $EQN is the equation of interest. For example, to run the wave equation run python3 run_inv.py wave.

Adding new equations

To define new equations, define a new dictionary with the following format:

eqn = {'eqn_type':equation name,
        'fcn':exact function,
        'domain':dictionary with keys of variables and values of lists with intervals,
        'dictionary':string of dictionary functions,
        'err_vec': vector to determine accuracy of estimation}

For more information on the algorithms described or if the code was useful, please check or cite the following paper:

Hasan, A., Pereira, J. M., Ravier, R., Farsiu, S., & Tarokh, V. (2020, May). 
Learning Partial Differential Equations From Data Using Neural Networks. 
In ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 3962-3966). IEEE.