A robust framework for identification of PDEs from noisy data

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields explainable machine learning. A critical challenge compared with general training that the term format are not known as a prior. In addition, significant measurement noise complex algorithm hyperparameter tuning usually reduces robustness existing methods. robust data-driven method proposed in this study identifying Partial Differential Equations (PDEs) given system from noisy data. The based on concept Progressive Sparse Identification PDEs (PSI-PDE or ψ-PDE). Special focus handling data huge uncertainties 50% level). Neural Network modeling fast Fourier transform (FFT) implemented to reduce influence sparse regression. Following this, candidate terms prescribed library progressively selected added learned PDEs, which automatically promotes parsimony respect number well their complexity. Next, significance each further evaluated coefficients PDE optimized by minimizing L2 residuals. Results numerical case studies indicate canonical dynamical systems can be correctly identified using ψ-PDE highly Codes all demonstrated examples available website: https://github.com/ymlasu. One benefit it avoids modification most Limitations major findings presented.