Electronic structure calculations involving a large number of electrons are computationally very demanding. For example, in the design of machine-learned interatomic potentials for materials or molecules, generating ab initio data for a large number of atomic configurations is often the most time-consuming part. Therefore, there is still a strong need in reducing the computational cost of such methods.
In this talk, I will present a recent work which aims at efficiently computing approximate solutions to eigenvalue problems parametrized by nuclei positions using a nonlinear reduced basis method based on optimal transport, so far for a toy model in 1D. Indeed, unlike in many applications where solutions for a given parameter can be efficiently approximated by linear combinations of solutions for other parameters, this approach does not work in electronic structure due to the localisation of the electronic density around the nuclei. However, by combining a sparse representation of the solution as a mixture of chosen functions with optimal transport methods, we manage to nicely approximate the solution of the problem. I will then discuss possible extensions to larger systems.
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