Statistical learning method for predicting density-matrix based electron dynamics

• URL: http://arxiv.org/abs/2108.00318v1
• Date: Sat, 31 Jul 2021 20:22:40 GMT
• Title: Statistical learning method for predicting density-matrix based electron dynamics
• Authors: Prachi Gupta, Harish S. Bhat, Karnamohit Ranka, Christine M. Isborn
• Abstract summary: We learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We can solve the Time-Dependent Hartree-Fock equation to propagate the electron density in time, and predict its dynamics for field-free and field-on scenarios. We observe close quantitative agreement between the predicted dynamics and ground truth for both field-off trajectories similar to the training data, and field-on trajectories outside of the training data.
• Score: 2.6763498831034034
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce dimensionality, while also exploiting regularization techniques like ridge regression for addressing multicollinearity. With the learned Hamiltonian we can solve the Time-Dependent Hartree-Fock (TDHF) equation to propagate the electron density in time, and predict its dynamics for field-free and field-on scenarios. We observe close quantitative agreement between the predicted dynamics and ground truth for both field-off trajectories similar to the training data, and field-on trajectories outside of the training data.

Related papers

• Enhanced coarsening of charge density waves induced by electron correlation: Machine-learning enabled large-scale dynamical simulations [4.94903410489486]
  phase ordering kinetics of emergent orders in correlated electron systems is a fundamental topic in non-equilibrium physics. We leverage modern machine learning (ML) methods to achieve a linear-scaling algorithm for simulating the coarsening of charge density waves (CDWs) Our study provides fresh insights into the role of electron correlations in non-equilibrium dynamics and underscores the promise of ML force-field approaches.
  arXiv  Detail & Related papers  (2024-12-30T16:44:11Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Accelerating Electron Dynamics Simulations through Machine Learned Time Propagators [0.9208007322096533]
  We present a novel approach to accelerate real time TDDFT based electron dynamics simulations. By leveraging physics-informed constraints and high-resolution training data, our model achieves superior accuracy and computational speed. This method has potential in enabling real-time, on-the-fly modeling of laser-irradiated molecules and materials.
  arXiv  Detail & Related papers  (2024-07-12T18:29:48Z)
• Self-Consistency Training for Density-Functional-Theory Hamiltonian Prediction [74.84850523400873]
  We show that Hamiltonian prediction possesses a self-consistency principle, based on which we propose self-consistency training. It enables the model to be trained on a large amount of unlabeled data, hence addresses the data scarcity challenge. It is more efficient than running DFT to generate labels for supervised training, since it amortizes DFT calculation over a set of queries.
  arXiv  Detail & Related papers  (2024-03-14T16:52:57Z)
• A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics [73.35846234413611]
  In drug discovery, molecular dynamics (MD) simulation provides a powerful tool for predicting binding affinities, estimating transport properties, and exploring pocket sites. We propose NeuralMD, the first machine learning (ML) surrogate that can facilitate numerical MD and provide accurate simulations in protein-ligand binding dynamics. We demonstrate the efficiency and effectiveness of NeuralMD, achieving over 1K$times$ speedup compared to standard numerical MD simulations.
  arXiv  Detail & Related papers  (2024-01-26T09:35:17Z)
• QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules [69.25826391912368]
  We generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 999 or 2998 molecular dynamics trajectories. We show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules.
  arXiv  Detail & Related papers  (2023-06-15T23:39:07Z)
• 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)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• 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)
• Inference of Stochastic Dynamical Systems from Cross-Sectional Population Data [8.905677748354364]
  Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. In this work, we deduce and then computationally estimate the Fokker-Planck equation which describes the evolution of the population's probability density, based on differential equations. Then, following the USDL approach, we project the Fokker-Planck equation to a proper set of test functions, transforming it into a linear system of equations.
  arXiv  Detail & Related papers  (2020-12-09T14:02:29Z)
• Machine Learning a Molecular Hamiltonian for Predicting Electron Dynamics [1.933681537640272]
  We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. The resulting Hamiltonians can be used for electron density evolution, producing highly accurate results even when propagating 1000 time steps beyond the training data.
  arXiv  Detail & Related papers  (2020-07-19T23:18:08Z)

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.