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Accelerating wavepacket propagation with machine learning.

Kanishka Singh1,2, Ka Hei Lee1,3, Daniel Peláez4

  • 1Theory of Electron Dynamics and Spectroscopy, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Berlin, Germany.

Journal of Computational Chemistry
|July 20, 2024
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Summary
This summary is machine-generated.

Fourier neural operators (FNOs) efficiently solve the time-dependent Schrödinger equation (TDSE), accurately modeling quantum wavepacket propagation. This machine learning approach accelerates simulations for inverse problems and control applications.

Keywords:
Fourier neural operatorsmachine learningquantum dynamics

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Area of Science:

  • Quantum mechanics
  • Machine learning
  • Computational physics

Background:

  • Traditional solvers for the time-dependent Schrödinger equation (TDSE) are computationally intensive.
  • Accurate quantum dynamical simulations are crucial for understanding and controlling molecular processes.

Purpose of the Study:

  • To introduce Fourier neural operators (FNOs) as an efficient alternative for solving the TDSE.
  • To demonstrate the accuracy and applicability of FNOs in quantum dynamics.
  • To explore FNOs for inverse problems and optimal control in quantum systems.

Main Methods:

  • Utilized Fourier neural operators (FNOs), a machine learning technique for approximating partial differential equations.
  • Applied FNOs to model wavepacket propagation in an anharmonic potential and a tunneling system.
  • Investigated the use of FNOs in conjunction with Markov-chain Monte Carlo for inverse problems.

Main Results:

  • FNOs accurately and faithfully model wavepacket propagation, including density evolution.
  • FNOs provide a significant speed-up compared to traditional TDSE solvers.
  • Demonstrated FNOs' suitability for repeated simulations in parameter optimization and control.

Conclusions:

  • Fourier neural operators offer an efficient and accurate method for solving the time-dependent Schrödinger equation.
  • FNOs can replace traditional solvers, particularly in applications requiring rapid simulations.
  • The speed advantage of FNOs enables advanced applications like optimal laser control and inverse problem solving.