Nathan Kutz: The Future of Governing Equations
Channel: Oxford ML and Physics Seminars
Date: 2022-02-11

Governing equations provide the technical language for our modern understanding of physics based systems. The derivation of governing equations is typically accomplished by leveraging physical principles such as symmetries, invariances, and/or conservation laws.  Governing equations efficiently specify the relationship between a state space variable and its temporal and spatial derivatives. To produce an estimate of the state space, governing equations must be simulated in order to produce any single realization of a given system.  Deep learning provides an alternative formulation of governing equations whereby neural networks can learn much more complex and comprehensive relationships between the state space and its derivatives. Moreover, deep learning models provide the potential for efficient encoding of physics while circumventing the need to simulate governing equations to produce an estimate of, for instance, a spatio-temporal trajectory. We will consider the use of deep learning for encoding physics, focusing on ideas of interpretability and physics-informed learning.  The goal is to use all the computational tools at our disposal, from scientific computing to neural networks, in order to accelerate the potential for physics modeling and discovery.