Scattering with Neural Operators

TL;DR

This paper explores the use of neural operators, specifically Fourier neural operators, to efficiently model quantum scattering processes, demonstrating their potential to outperform traditional solvers in physics simulations.

Contribution

It introduces an iterated Fourier neural operator approach for learning Schrödinger operators and applies it to quantum scattering problems in multiple dimensions.

Findings

Neural operators can accurately predict wave function evolution.

They offer significant computational efficiency over finite-difference methods.

Successful application to 1+1 and 2+1 dimensional scattering scenarios.

Abstract

Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we examine applications to scattering processes in quantum mechanics. We use an iterated variant of Fourier neural operators to learn the physics of Schr\"odinger operators, which map from the space of initial wave functions and potentials to the final wave functions. These deep operator learning ideas are put to test in two concrete problems: a neural operator predicting the time evolution of a wave packet scattering off a central potential in $1+1$ dimensions, and the double-slit experiment in $2+1$ dimensions. At inference, neural operators can become orders of magnitude more efficient compared to traditional finite-difference solvers.