Prof. Nathan Kutz from the University of Washington, will present a talk at the Applied Mathematics Colloquium.
Title: Discovery of Dynamical Models from Data
Abstract: Machine learning and artificial intelligence algorithms are now being used to automate the discovery of governing physical equations and coordinate systems from measurement data alone. However, positing a universal physical law from data is challenging: (i) An appropriate coordinate system must also be advocated and (ii) simultaneously proposing an accompanying discrepancy model to account for the inevitable mismatch between theory and measurements must be considered. Using a combination of deep learning and sparse regression, specifically the sparse identification of nonlinear dynamics (SINDy) algorithm, we show how a robust mathematical infrastructure can be formulated for simultaneously learning physics models and their coordinate systems. This can be done with limited data and sensors. We demonstrate the methods on a diverse number of examples, showing how data can maximally be exploited for scientific and engineering applications.
Bio: Nathan Kutz is the Yasuko Endo and Robert Bolles Professor of Applied Mathematics at the University of Washington, having served as chair of the department from 2007-2015. He has a wide range of interests, including neuroscience to fluid dynamics where he integrates machine learning with dynamical systems and control.
His research interests focus on numerical methods and scientific computing, data analysis and dimensionality reduction (PCA, POD, etc) methods, dynamical systems, bifurcation theory, linear and nonlinear wave propagation, perturbation and asymptotic methods, nonlinear analysis, variational methods, soliton theory, nonlinear optics, mode-locked lasers, fluid dynamics, Bose-Einstein condensation, neuroscience, gesture recognition and video & image processing.
Host: Amir Sagiv