The so-called curse of dimensionality plagues high-dimensional computational algorithms. Conventionally, applied mathematicians have turned to linear algebra techniques to find low-rank matrix approximations which can be substituted gainfully into rate-limiting algorithmic operations.  And though this technique finds much success, the application of linear algebra to higher-order tensors is not so straightforward.  In this work, I investigate the use of multilinear algebra and higher-order decompositions to reduce the complexity of high-dimensional algorithms in quantum physics and chemistry applications. Here I will demonstrate how I have used these approaches to develop a number of novel reduced-scaling electronic structure methods and to construct approximate methods for contracting high-order tensor networks.

About the speaker

I am currently a Postdoctoral Research Fellow at the Flatiron Institute's Center for Computational Quantum Physics. My research focuses on application of the canonical polyadic decomposition to accurate electronic structure methods, particularly coupled cluster methods. I am interested in reduced-scaling algorithms, novel applications of tensor decompositions and high-performance and heterogeneous computing algorithms. I finished my PhD at Virginia Tech with Dr. Edward Valeev in December 2021 where I focused on implementation of the canonical polyadic decomposition algorithms and the decompositions application to wavefunction methods. I have been a postdoc at the Flatiron Institute since September 2022 where I have primarily focused on the development of the tensor algebra package ITensors.jl.