Machine-learning Kohn-Sham potential from dynamics in time-dependent Kohn-Sham systems

• URL: http://arxiv.org/abs/2207.00687v2
• Date: Mon, 21 Aug 2023 18:54:23 GMT
• Title: Machine-learning Kohn-Sham potential from dynamics in time-dependent Kohn-Sham systems
• Authors: Jun Yang, James D Whitfield
• Abstract summary: We propose a machine learning method to develop the energy functional and the Kohn-Sham potential of a time-dependent Kohn-Sham system. The method is based on the dynamics of the Kohn-Sham system and does not require any data on the exact Kohn-Sham potential for training the model.
• Score: 3.4619244960577435
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn-Sham potential of a time-dependent Kohn-Sham system is proposed. The method is based on the dynamics of the Kohn-Sham system and does not require any data on the exact Kohn-Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D two-electron example. We show that the machine-learned Kohn-Sham potential matches the exact Kohn-Sham potential in the absence of memory effect. Our method can still capture the dynamics of the Kohn-Sham system in the presence of memory effects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn-Sham potential in the time-dependent Kohn-Sham system.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• NeuralSCF: Neural network self-consistent fields for density functional theory [1.7667864049272723]
  Kohn-Sham density functional theory (KS-DFT) has found widespread application in accurate electronic structure calculations. We propose a neural network self-consistent fields (NeuralSCF) framework that establishes the Kohn-Sham density map as a deep learning objective.
  arXiv  Detail & Related papers  (2024-06-22T15:24:08Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Deep learning of spatial densities in inhomogeneous correlated quantum systems [0.0]
  We show that we can learn to predict densities using convolutional neural networks trained on random potentials. We show that our approach can handle well the interplay of interference and interactions and the behaviour of models with phase transitions in inhomogeneous situations.
  arXiv  Detail & Related papers  (2022-11-16T17:10:07Z)
• Revealing microcanonical phase diagrams of strongly correlated systems via time-averaged classical shadows [0.0]
  We propose a method to study microcanonical phases and phase transitions on a quantum computer from quantum dynamics. We first show that this method, applied to ground state calculations on 100 qubit systems, discovers the geometric relationship between magnetization and field. We then show that diffusion maps of TACS data from quantum dynamics simulations efficiently learn the phase-defining features and correctly identify the quantum critical region.
  arXiv  Detail & Related papers  (2022-11-02T16:39:52Z)
• Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials [77.34726150561087]
  We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
  arXiv  Detail & Related papers  (2022-10-03T16:51:25Z)
• Port-Hamiltonian Neural Networks with State Dependent Ports [58.720142291102135]
  We stress-test the method on both simple mass-spring systems and more complex and realistic systems with several internal and external forces. Port-Hamiltonian neural networks can be extended to larger dimensions with state-dependent ports. We propose a symmetric high-order integrator for improved training on sparse and noisy data.
  arXiv  Detail & Related papers  (2022-06-06T14:57:25Z)
• Machine learning for excitation energy transfer dynamics [0.0]
  We use the hierarchical equations of motion (HEOM) to simulate open quantum dynamics in the biological regime. We generate a set of time dependent observables that depict the coherent propagation of electronic excitations through the light harvesting complexes. We demonstrate the capability of convolutional neural networks to tackle this research problem.
  arXiv  Detail & Related papers  (2021-12-22T14:11:30Z)
• Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System [2.6763498831034034]
  We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent Schr"odinger equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential.
  arXiv  Detail & Related papers  (2021-12-14T00:01:19Z)
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation [77.34726150561087]
  We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts. We discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor.
  arXiv  Detail & Related papers  (2021-06-25T17:25:38Z)
• Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla [50.002949299918136]
  We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system suitable to implement quantum computation algorithms. It embeds an electronic spin 1/2 coupled through hyperfine interaction to a nuclear spin 7/2, both characterized by remarkable coherence.
  arXiv  Detail & Related papers  (2021-03-15T21:38:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.