Title: Operator Learning in Seismology: AI for infinite dimensions

Abstract:

Seismology and geophysics are fields in which phenomena are typically described by partial differential equations, i.e. operators that map between infinite dimensional function spaces. However, deep neural networks are designed to work only on finite dimensional vector spaces. An immediate consequence is that deep neural networks are trained for a particular spatial/temporal discretization, and are unable to generalize to arbitrary mesh configurations. For example, suddenly increasing the spatial resolution by 1000x can break deep neural networks, even if the physics is the same at both scales. A recent machine learning paradigm called Operator Learning has developed a variety of Neural Operator models that naturally learn on function spaces, and provably generalize to irregular sensor geometries and arbitrary mesh resolution. This makes Neural Operators an excellent choice for many data-driven and simulation-based problems. In this talk, I will cover the fundamentals of Operator Learning and its importance to problems in seismology and geophysics. I will show applications to earthquake detection and picking; applications to seismic full waveform imaging; generative modeling of seismic ground motions, and more. I will highlight the advantages of using Neural Operators instead of Neural Networks for each of these problems. I will discuss why I believe Operator Learning will be a valuable part of Seismology in the future.