Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System

• URL: http://arxiv.org/abs/2112.07067v1
• Date: Tue, 14 Dec 2021 00:01:19 GMT
• Title: Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System
• Authors: Harish S. Bhat and Kevin Collins and Prachi Gupta and Christine M. Isborn
• Abstract summary: 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.
• Score: 2.6763498831034034
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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; this yields electron densities suitable for training models of the correlation potential. We frame the learning problem as one of optimizing a least-squares objective subject to the constraint that the dynamics obey the TDKS equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential. Our results show that it is possible to learn values of the correlation potential such that the resulting electron densities match ground truth densities. We also show how to learn correlation potential functionals with memory, demonstrating one such model that yields reasonable results for trajectories outside the training set.

Related papers

• Inferring Relational Potentials in Interacting Systems [56.498417950856904]
  We propose Neural Interaction Inference with Potentials (NIIP) as an alternative approach to discover such interactions. NIIP assigns low energy to the subset of trajectories which respect the relational constraints observed. It allows trajectory manipulation, such as interchanging interaction types across separately trained models, as well as trajectory forecasting.
  arXiv  Detail & Related papers  (2023-10-23T00:44:17Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• 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)
• Learning Pair Potentials using Differentiable Simulations [1.9950682531209156]
  We propose a general method for learning pair interactions from data using differentiable simulations (DiffSim) DiffSim defines a loss function based on structural observables, such as the radial distribution function, through molecular dynamics (MD) simulations. The interaction potentials are then learned directly by gradient descent, using backpropagation to calculate the gradient of the structural loss metric.
  arXiv  Detail & Related papers  (2022-09-16T02:36:02Z)
• Machine-learning Kohn-Sham potential from dynamics in time-dependent Kohn-Sham systems [3.4619244960577435]
  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.
  arXiv  Detail & Related papers  (2022-07-01T23:22:50Z)
• Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles [0.0]
  We use Diffusion Maps (a manifold learning algorithm) to identify a set of useful latent observables. We show that the obtained variables and the learned dynamics accurately encode physics of the Brownian Dynamic Simulations. Our dimension reduction/reduced model identification approach can be easily ported to a broad class of particle systems dynamics experiments/models.
  arXiv  Detail & Related papers  (2022-04-30T14:58:25Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• DiffPD: Differentiable Projective Dynamics with Contact [65.88720481593118]
  We present DiffPD, an efficient differentiable soft-body simulator with implicit time integration. We evaluate the performance of DiffPD and observe a speedup of 4-19 times compared to the standard Newton's method in various applications.
  arXiv  Detail & Related papers  (2021-01-15T00:13:33Z)
• Machine learning dynamics of phase separation in correlated electron magnets [0.0]
  We demonstrate machine-learning enabled large-scale dynamical simulations of electronic phase separation in double-exchange system. Our work paves the way for large-scale dynamical simulations of correlated electron systems using machine-learning models.
  arXiv  Detail & Related papers  (2020-06-07T17:01:06Z)
• Convolutional Tensor-Train LSTM for Spatio-temporal Learning [116.24172387469994]
  We propose a higher-order LSTM model that can efficiently learn long-term correlations in the video sequence. This is accomplished through a novel tensor train module that performs prediction by combining convolutional features across time. Our results achieve state-of-the-art performance-art in a wide range of applications and datasets.
  arXiv  Detail & Related papers  (2020-02-21T05:00:01Z)

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.