Siwar Badreddine

PhD candidate in Inria Paris and Sorbonne university

I’m currently in my final year of pursuing a Ph.D. at Inria Paris and Sorbonne University. My research focuses on low-rank tensor decomposition techniques to address complex high-dimensional problems in quantum chemistry. These challenges typically involve managing large datasets that can be represented by tensors. My work revolves around improving and developing algorithms involved in solving the time-independent Schrödinger equation for the ground-state search. Specifically, I’m interested in studying approaches like Density Matrix Renormalization Group (DMRG) / Alternating Least Squares (ALS) for solving high-dimensional eigenvalue problems using tensor train decomposition methods.

Projects

LTEI_TA

The long-range Coulomb potential is a significant factor in molecular simulations, and its accurate evaluation is essential for accurate results. The present study proposes an approximation method for the numerical evaluation of the long-range Coulomb potential and the approximation of the resulting high-dimensional Two-Electron Integrals (TEI) tensor with long-range interactions. This method is based on the tensorized structure of the compressed two-electron integrals, which are obtained through two-dimensional Chebyshev interpolation combined with Gaussian quadrature. This is a prototype implementation in the Julia programming language.

SCATensorPack

A package in Julia that aims to implement ALS and MALS algorithms (known in quantum Chemistry as DMRG) with efficient construction of ab initio Hamiltonian operators and eigenfunctions using a block sparse tensor train representation, optimized algorithms for performing block sparse tensor contractions, a critical operation in quantum chemistry computations, efficient compression of block sparse tensors, helping manage memory and computational resources efficiently (ongoing work).