This was part of Expressing and Exploiting Structure in Modeling, Theory, and Computation with Gaussian Processes

Physics-Informed Learning Machines

Maziar Raissi, University of Colorado Boulder
Friday, September 2, 2022



Abstract:
A grand challenge with great opportunities is to develop a coherent framework that enables blending conservation laws, physical principles, and/or phenomenological behaviors expressed by differential equations with the vast data sets available in many
fields of engineering, science, and technology. At the intersection of probabilistic machine learning, deep learning, and scientific
computations, this work is pursuing the overall vision to establish promising new directions for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data. To materialize this vision, this work is exploring two complementary directions: (1) designing data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and non-linear differential equations, to extract patterns from high-dimensional data
generated from experiments, and (2) designing novel numerical algorithms that can seamlessly blend equations and noisy
multi-fidelity data, infer latent quantities of interest (e.g., the solution to a differential equation), and naturally quantify
uncertainty in computations.