Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Home 
 People 
 Current 
 Executive Committee 
 Postdocs 
 Visitors 
 Students 
 Research 
 Publications 
 Conferences 
 Workshops 
 Sponsorship 
 Talks 
 Seminars 
 Postdoc Seminars Archive 
 Quantum Lunch 
 Quantum Lunch Archive 
 P/T Colloquia 
 Archive 
 Ulam Scholar 
 
 Postdoc Nominations 
 Student Requests 
 Student Program 
 Visitor Requests 
 Description 
 Past Visitors 
 Services 
 General 
 
 History of CNLS 
 
 Maps, Directions 
 CNLS Office 
 T-Division 
 LANL 
 
Thursday, July 27, 2023
10:00 AM - 11:00 AM
CNLS Conference Room (TA-3, Bldg 1690)

Seminar

The Adaptive Spectral Koopman Method for Scientific Computing

Xiu Yang
Lehigh University

We propose the adaptive spectral Koopman (ASK) method to solve nonlinear autonomous dynamical systems. This novel numerical method leverages the spectral-collocation method and properties of the Koopman operator to obtain the solution of a dynamical system. Specifically, this solution is represented by Koopman operator's eigenfunctions, eigenvalues, and Koopman modes. Unlike conventional time evolution algorithms such as Euler's scheme and the Runge-Kutta scheme, ASK is mesh-free, and hence is more flexible when evaluating the solution. Numerical experiments demonstrate high accuracy of ASK for solving both ordinary and partial differential equations. Further, ASK enables new designs of uncertainty quantification (UQ) methods, which can be much faster than state-of-the-art UQ methods. Finally, we will illustrate ASK's capability of solving optimization problems based on the gradient flow formula.

Bio Xiu Yang obtained his bachelor and master degree in Peking University, and his Ph.D. from Brown University. He joined Lehigh University from Pacific Northwest National Laboratory (PNNL) where he was a scientist since 2016. His research has been centered around modern scientific computing including uncertainty quantification, multi-scale modeling, physics-informed machine learning, and data-driven scientific discovery. Xiu has been applying his methods on various research areas such as fluid dynamics, hydrology, biochemistry, soft material, climate modeling, energy storage, and power grid system. Currently, he is focusing on uncertainty quantification in quantum computing algorithms and machine learning methods for scientific computing. He received a Faculty Early Career Development Program (CAREER) Award from NSF in 2022 and Outstanding Performance Award from PNNL in 2015 and 2016. Xiu also served on the DOE applied mathematics visioning committee in 2019.

Host: Youzuo Lin