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  • Letter
  • Open Access

Scattering with neural operators

Sebastian Mizera

  • Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA

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Phys. Rev. D 108, L101701 – Published 16 November, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L101701

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 Schrödinger 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 out-of-distribution 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.

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Outline

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Phys. Rev. D 108, L101701– Published 16 November, 2023
  • Received 31 August 2023
  • Accepted 23 October 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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