Upcoming Event: CSEM Student Forum

Harnessing High-Order Derivatives for Tensor-Network Surrogates of PDE-Constrained Maps

Blake Christierson, CSEM Student

Abstract

Many surrogates leverage local low rank approximations of the Jacobian (and some the Hessian). These represent first and second order sensitivity information; however, many problems have rich higher order sensitivity information that is crucial to creating a faithful surrogate for the system of interest. I will present ongoing work into global polynomial surrogates informed by high order sensitivities. The method addresses the major roadblock of the curse of dimensionality by representing the global polynomial as a Tucker tensor train which is constructed matrix-free from randomized symmetric derivative actions. If time permits, I will share preliminary results using the surrogate to sample the posterior of a nonlinear diffusion reaction Bayesian inverse problem and also provide some tips on generating figures via tikzplotlib.