Effective Many-body Interactions in Reduced-Dimensionality Spaces Through Neural Network Models

• URL: http://arxiv.org/abs/2407.05536v1
• Date: Mon, 8 Jul 2024 00:56:24 GMT
• Title: Effective Many-body Interactions in Reduced-Dimensionality Spaces Through Neural Network Models
• Authors: Senwei Liang, Karol Kowalski, Chao Yang, Nicholas P. Bauman,
• Abstract summary: We develop a framework that integrates recent advances in the development of active-space representations of Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugen diagrams. We demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate/ extrapolate their forms to other geometrical configurations.
• Score: 4.955567578189708
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head-on. Therefore, developing reduced dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper, we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded/effective Hamiltonians. Using small molecular systems (the H2O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate/ extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces.

Related papers

• Denoising Hamiltonian Network for Physical Reasoning [41.88573341335723]
  Denoising Hamiltonian Network (DHN) is a novel framework that generalizes Hamiltonian mechanics operators into more flexible neural operators. DHN captures non-local temporal relationships and mitigates numerical integration errors through a denoising mechanism. We demonstrate its effectiveness and flexibility across three diverse physical reasoning tasks with distinct inputs and outputs.
  arXiv  Detail & Related papers  (2025-03-10T17:57:01Z)
• Exploring the Nexus of Many-Body Theories through Neural Network Techniques: the Tangent Model [4.955567578189708]
  We present a physically informed neural network representation of the effective interactions associated with coupled-cluster downfolding models. The representation allows us to evaluate the effective interactions efficiently for various geometrical configurations of chemical systems.
  arXiv  Detail & Related papers  (2025-01-27T05:36:55Z)
• Artificial Kuramoto Oscillatory Neurons [65.16453738828672]
  We introduce Artificial Kuramotoy Neurons (AKOrN) as a dynamical alternative to threshold units. We show that this idea provides performance improvements across a wide spectrum of tasks. We believe that these empirical results show the importance of our assumptions at the most basic neuronal level of neural representation.
  arXiv  Detail & Related papers  (2024-10-17T17:47:54Z)
• Integrating GNN and Neural ODEs for Estimating Non-Reciprocal Two-Body Interactions in Mixed-Species Collective Motion [0.0]
  We present a novel deep learning framework for estimating the underlying equations of motion from observed trajectories. Our framework integrates graph neural networks with neural differential equations, enabling effective prediction of two-body interactions.
  arXiv  Detail & Related papers  (2024-05-26T09:47:17Z)
• Robust Hamiltonian Engineering for Interacting Qudit Systems [50.591267188664666]
  We develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. We experimentally demonstrate these techniques in a strongly-interacting, disordered ensemble of spin-1 nitrogen-vacancy centers.
  arXiv  Detail & Related papers  (2023-05-16T19:12:41Z)
• Solving the nuclear pairing model with neural network quantum states [58.720142291102135]
  We present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism. A memory-efficient version of the reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian.
  arXiv  Detail & Related papers  (2022-11-09T00:18:01Z)
• Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model [0.0]
  We analytically illustrate that hitherto unexplored imaginary components of out-of-time correlators can provide unprecedented insight into the information scrambling capacity of a graph neural network. Such an analysis demystifies the training of quantum machine learning models by unraveling how quantum information is scrambled through such a network.
  arXiv  Detail & Related papers  (2022-08-29T06:17:28Z)
• Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks [72.09574528342732]
  Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs) They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
  arXiv  Detail & Related papers  (2022-06-29T19:03:10Z)
• A2I Transformer: Permutation-equivariant attention network for pairwise and many-body interactions with minimal featurization [0.1469945565246172]
  In this work, we suggest an end-to-end model which directly predicts per-atom energy from the coordinates of particles. We tested our model against several challenges in molecular simulation problems, including periodic boundary condition (PBC), $n$-body interaction, and binary composition.
  arXiv  Detail & Related papers  (2021-10-27T12:18:25Z)
• Solving the electronic Schr\"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks [4.1201966507589995]
  We introduce a weight-sharing constraint when optimizing neural network-based models for different molecular geometries. We find that this technique can accelerate optimization when considering sets of nuclear geometries of the same molecule by an order of magnitude.
  arXiv  Detail & Related papers  (2021-05-18T08:23:09Z)
• Large-scale Neural Solvers for Partial Differential Equations [48.7576911714538]
  Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. Recent numerical solvers require manual discretization of the underlying equation as well as sophisticated, tailored code for distributed computing. We examine the applicability of continuous, mesh-free neural solvers for partial differential equations, physics-informed neural networks (PINNs) We discuss the accuracy of GatedPINN with respect to analytical solutions -- as well as state-of-the-art numerical solvers, such as spectral solvers.
  arXiv  Detail & Related papers  (2020-09-08T13:26:51Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)
• Graph Neural Network for Hamiltonian-Based Material Property Prediction [56.94118357003096]
  We present and compare several different graph convolution networks that are able to predict the band gap for inorganic materials. The models are developed to incorporate two different features: the information of each orbital itself and the interaction between each other. The results show that our model can get a promising prediction accuracy with cross-validation.
  arXiv  Detail & Related papers  (2020-05-27T13:32:10Z)
• Disorder-controlled relaxation in a 3D Hubbard model quantum simulator [0.4215938932388722]
  We study the relaxation dynamics of doubly occupied lattice sites in the disordered Fermi-Hubbard model (DFHM) In addition to observing the widely studied effect of disorder inhibiting relaxation, we find that the cooperation between strong interactions and disorder also leads to the emergence of a dynamical regime characterized by textitdisorder-enhanced relaxation. Our results provide a theoretical framework for a previously inaccessible regime of the DFHM and demonstrate the ability of quantum simulators to enable understanding of complex many-body systems.
  arXiv  Detail & Related papers  (2020-01-21T04:40:15Z)

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.