The University of Arizona: Modeling, Computation, Nonlinearity, Randomness and Waves Seminar – Dynamic tensor approximation of nonlinear PDEs

Presenter: Daniele Venturi, Engineering, University of California – Santa Cruz

Recently, there has been a growing interest in approximating nonlinear functions and PDEs on tensor manifolds. The reason is simple: tensors can drastically reduce the computational cost of high-dimensional problems when the solution has a low-rank structure. In this talk, I will review recent developments on rank-adaptive algorithms for temporal integration of PDEs on tensor manifolds. Such algorithms combine functional tensor train (FTT) series expansions, operator splitting time integration, and an appropriate criterion to adaptively add or remove tensor modes from the FTT representation of the PDE solution as time integration proceeds. I will also present a new tensor rank reduction method that leverages coordinate flows. The idea is very simple: given a multivariate function, determine a coordinate transformation so that the function in the new coordinate system has a smaller tensor rank. I will restrict the analysis to linear coordinate transformations, which give rise to a new class of functions that we refer to as tensor ridge functions. Numerical applications are presented and discussed for linear and nonlinear advection equations, and for the Fokker-Planck equation.

SHORT BIO: Dr. Venturi is a professor of Applied Mathematics in the Baskin School of Engineering at UC Santa Cruz. He received his MS in Mechanical Engineering in 2002, and his PhD in Applied Physics in 2006 from the University of Bologna (Italy). His research activity has been recently focused on the numerical approximation of PDEs on tensor manifolds, including high-dimensional PDEs arising from the discretization of functional differential equations (infinite-dimensional PDEs).



LOCATIONS: Math, 402 and Zoom  Password:  applied

  • Audience: Adult, STEM Professional
  • Genre: Mathematics
  • Type: Exhibit/Presentation


Apr 13 2023


12:30 pm - 1:30 pm



More Info

Register Here


Pima STEM Hub


Hybrid (Online & In-person)

Location 2

The University of Arizona Mathematics Building
617 N. Santa Rita Ave., Tucson, AZ, 85721


The University of Arizona College of Mathematics
(520) 621-6866
Register Here
QR Code