Nonlinear reduced models for guaranteed and efficient calculations in quantum chemistry – NUMERIQ

Numerical simulations performed for modelling molecular and materials systems are costly and represent a large part of the calculations run on supercomputers (around 35%). The aim of this project is to develop
fast and reliable methods in this field, through the design and development of nonlinear reduced models relying on recent data-driven techniques such as using explicit nonlinear transformations and optimal transport.
More precisely, we will be interested in the solutions of electronic structure calculations equations, which are mathematically speaking -possibly nonlinear- eigenvalue elliptic partial differential equations, parametrized by the positions of the nuclei in the molecular or material system of interest. We are interested in the context where these equations have to be solved a large number of times for different positions of the nuclei.
Due to the particular structure of the solutions, traditional linear reduced basis methods typically used in this context do not work well.
Therefore, we intend to develop nonlinear reduced models for this problem with guaranteed accuracy, which requires to develop error bounds for these reduced models. We believe that methods based on explicit well-chosen transformations and optimal transport could achieve this, provided that such tools are correctly adapted and developed for the problem under consideration and that error guarantees are derived for the new methods.
Thus, the proposed project should lead to faster and more reliable electronic structure calculations than what is available today.