Use Case DESY III

Spectral Deep-Learning for Solving Differential Equations: Schrödinger Equation as an Example

Date:
13.09.2022, 15:30 - 17:00
Duration:
90 minutes
Location:
H 0.009

Abstract

Neural networks have been very successful in approximating high-dimensional functions in applications ranging from computer vision to natural language processing. Recently, neural networks emerged as a promising tool to approximate solutions of partial differential equations, which is of vital importance to natural sciences. Methods employing neural networks were shown to be free from the curse of dimensionality in some cases. However, these methods are far from reliable for solving differential equations because of the lack of convergence guarantees and training instabilities.

In this talk we demonstrate how to use neural networks to solve the Schrödinger equation that describes the vibrational motion of molecules. In particular, we show that normalising flows are a promising tool because accurate numerical results as well as convergence guarantees can be obtained. We further outline the prospective of using these methods to describe the laser-induced dynamics of weakly-bound molecules.

Yahya Saleh
DESY/UHH
J. Eggers
DESY/UHH
Vishnu Sanjay
Gran Science Institute (GSSI)
A. Iske
University of Hamburg
A. Yachmenev
DESY/UHH
J. Küpper
DESY/UHH