Approximation and Learning Density Matrices

PN 3-14

Project Description

In this project, we investigate the manipulation, approximation, and learning of density matrices arising in electronic structure calculation in computational chemistry, material science, and solid-state physics. Electronic structure calculation aims at finding the state of the electrons of a given molecular system specified by the nuclear coordinates. The density matrix can be seen as the solution to the governing non-linear eigenvalue problem in the context of Density-Functional Theory (DFT). Therefore, there is an intrinsic map between the nuclear coordinates and the corresponding density matrix. A key challenge is thus to learn this map and/or to interpolate between given density matrices along given reaction coordinates. One challenge is that the set of admissible densities is a non-linear, but differential, manifold that is isomorphic to the Grassmann manifold. We will use tools from computational differential geometry to propose approximate density matrices that lie exactly on the manifold.

Project Information

Project Number PN 3-14
Project Name Approximation and Learning Density Matrcies
Project Duration March 2023 - December 2025
Project Leader Benjamin Stamm
Project Members Zahra Askarpour, PhD Researcher
Project Partners Johannes Kästner
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