LANS Seminar

Seminar Title: Tucker tensor train Taylor series approximation of high dimensional implicit mappings

Speaker: Nick Alger,Researcher, Oden Institute, UT Austin Working on Numerical Methods for Solving Inverse Problems Governed by PDEs

Date: Thursday, September 25, 2025

Time: 2:30 PM-3:30 PM (In-Person)

Location: Hybrid, Bldg. 240, Conference Room 4301

Host: Vishwas Rao

Description: We present an efficient method for constructing high order Taylor series surrogate models for high dimensional mappings that depend implicitly on the solution of a system of nonlinear equations, e.g., a partial differential equation. High order Taylor series are traditionally considered intractable here because the derivative tensors are extremely large, and are only accessible through multilinear actions on vectors. We overcome these challenges using a “Tucker tensor train Taylor series” surrogate model, in which linear (Tucker) dimension reduction is performed on the input and output spaces, and the derivative tensors are approximated by tensor trains in the reduced subspaces. The Tucker bases are constructed using randomized sketching, and the tensor trains are fit to directionally symmetric action data using a Riemannian manifold Newton method. We justify the model theoretically, and provide numerical evidence for the effectiveness of the proposed method.

Bio: Nick Alger is a researcher in the Oden Institute at UT Austin working on numerical methods for solving inverse problems governed by PDEs. He received his Ph.D. and M.S. in computational science from UT Austin, and B.S. in physics from Harvey Mudd College.

Please note that the meeting URL for this event can be seen on the cels-seminars website which requires an Argonne login.