Data-driven discovery of Green's functions with human-understandable deep learning
This enables scientists to accelerate discovery by interpreting deep learning results, though it is incremental in applying existing neural network techniques to a specific domain.
The authors tackled the problem of making deep learning findings interpretable in scientific contexts by developing a data-driven method to learn Green's functions from physical system responses, revealing properties like conservation laws and symmetries with examples in advection-diffusion and Stokes flow.
There is an opportunity for deep learning to revolutionize science and technology by revealing its findings in a human interpretable manner. To do this, we develop a novel data-driven approach for creating a human-machine partnership to accelerate scientific discovery. By collecting physical system responses under excitations drawn from a Gaussian process, we train rational neural networks to learn Green's functions of hidden linear partial differential equations. These functions reveal human-understandable properties and features, such as linear conservation laws and symmetries, along with shock and singularity locations, boundary effects, and dominant modes. We illustrate the technique on several examples and capture a range of physics, including advection-diffusion, viscous shocks, and Stokes flow in a lid-driven cavity.