Data-driven discovery of Green's functions with human-understandable deep learning.

Area of Science:

• Artificial Intelligence
• Computational Physics
• Scientific Discovery

Background:

• Deep learning offers potential to revolutionize science by providing human-interpretable findings.
• Current methods often lack transparency, hindering scientific progress.

Purpose of the Study:

• To develop a novel data-driven approach for a human-machine partnership to accelerate scientific discovery.
• To create interpretable models of physical systems using deep learning.

Main Methods:

• Collected physical system responses under Gaussian process excitations.
• Trained rational neural networks to learn Green's functions of hidden linear partial differential equations.
• Analyzed learned functions for human-understandable properties.

Main Results:

• Identified human-understandable properties such as linear conservation laws and symmetries.
• Located shock and singularity points, boundary effects, and dominant modes.
• Successfully applied the technique to advection-diffusion, viscous shocks, and Stokes flow.

Conclusions:

• The developed approach enables a human-machine partnership for accelerated scientific discovery.
• Rational neural networks can learn interpretable Green's functions from data.
• This method reveals key physical properties and system behaviors in a human-understandable format.