Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data

Area of Science:

• Chemical Engineering
• Computational Science
• Applied Mathematics

Background:

• Discovering governing equations for complex systems is crucial for scientific advancement.
• Traditional methods struggle with scarce and noisy experimental data.
• Partial Differential Equations (PDEs) are fundamental in modeling many physical phenomena.

Purpose of the Study:

• To develop a novel framework for identifying free-form PDEs from scarce and noisy data.
• To demonstrate the framework's effectiveness on synthetic systems.
• To compare its performance against existing methods like weak Sparse Identification of Nonlinear Dynamics (SINDy).

Main Methods:

• Symbolic regression utilizing genetic programming.
• Time-variant data collection from synthetic systems.
• Comparative analysis with weak SINDy.

Main Results:

• Successfully identified ground truth PDE models for four synthetic systems.
• Demonstrated superior performance over weak SINDy in data-scarce scenarios.
• Showcased robustness to noise and data scarcity, recovering models from minimal data points (8 time series) with up to 50% noise.

Conclusions:

• The proposed framework effectively identifies meaningful PDE models even with limited and noisy data.
• It offers a robust solution for PDE discovery where data acquisition is challenging or costly.
• This approach holds significant potential for advancing scientific discovery in data-limited fields.