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MO: Fachverband Molekülphysik

MO 7: Machine Learning and Computational and Theoretical Molecular Physics

MO 7.1: Hauptvortrag

Mittwoch, 8. März 2023, 11:00–11:30, F142

Augmenting basis with normalizing flows for solving Schrödinger equations: theoretical analysis — •Yahya Saleh^1,2, Armin Iske², Andrey Yachmenev^1,4, and Jochen Küpper^1,3,4 — ¹Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Hamburg — ²Department of Mathematics, Universität Hamburg — ³Department of Physics, Universität Hamburg — ⁴for Ultrafast Imaging, Universität Hamburg

Spectral methods are a popular class for solving time-independent Schrödinger equations. Here, one approximates the wavefunctions in the linear span of standard basis sets of L2. In spite of the well-posedness and the convergence guarantees of such methods, they suffer from the curse of dimenionality, as the computational expenses grow exponentially with the size of the quantum system.

Recently, nonlinear functions, e.g., neural networks have been proposed to model ground states and low-lying excited states of Schrödinger equations. Although they promise accurate results with smaller scaling than standard methods, extensions of such models to the simultaneous computation of many states are still lacking.

Here, we propose to model excited states of Schrödinger equations via augmented basis sets, where standard basis sets are composed with normalizing flows. We show that such a numerical scheme is well-posed and defines a richer approximation space than standard methods. Moreover, we provide convergence guarantees.