Deep learning architectures for science and engineering
A major challenge in the study of science and engineering systems is that of model discovery: turning data into reduced order models that are not just predictive but provide insight into the nature of the underlying dynamical system that generated the data. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their embeddings from data.

We consider two canonical cases: (i) systems for which we have full measurements of the governing variables, and (ii) systems for which we have incomplete measurements. For systems with full state measurements, we show that the recent sparse identification of nonlinear dynamical systems (SINDy) method can discover governing equations with relatively little data and introduce a sampling method that allows SIN Dy to scale efficiently to problems with multiple time scales, noise and parametric dependencies. For systems with incomplete observations, we show that the Hankel alternative view of Koopman (HAVOK) method, based on time-delay embedding coordinates and the dynamic mode decomposition, can be used to obtain a linear models and Koopman invariant measurement systems that nearly perfectly captures the dynamics of nonlinear quasiperiodic systems.

Neural networks are used in targeted ways to aid in the model reduction process. Together, these approaches provide a suite of mathematical strategies for reducing the data required to discover and model nonlinear multiscale systems.

Brief Biography:
J. Nathan Kutz received the B.S. degree in physics and mathematics from the University of Washington, Seattle, WA, USA, in 1990, and the Ph.D. degree in applied mathematics from Northwestern University, Evanston, IL, USA, in 1994. He is currently the Director of the AI Institute in
Dynamics Systems, the Boeing Professor of AI and Data-Driven Engineering, Professor of applied mathematics and electrical engineering, and a Senior Data Science Fellow with the eScience Institute, University of Washington.
Date: 28 November 2024, 16:00 (Thursday, 7th week, Michaelmas 2024)
Venue: Mathematical Institute, Woodstock Road OX2 6GG
Venue Details: Lecture Room 1
Speaker: J Nathan Kutz (University of Washington)
Organising department: Department of Materials
Organiser: Luci Bywater (Department of Materials, Advanced Nanoscale Engineering Group)
Organiser contact email address: lucinda.bywater@materials.ox.ac.uk
Host: Professor Harish Bhaskaran (Department of Materials and Advanced Nanoscale Engineering Group)
Booking required?: Not required
Audience: Members of the University only
Editor: Lorraine Laird