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.
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.