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Solving Many-Electron Schrödinger Equation Using Deep Neural Networks [article]

Jiequn Han, Linfeng Zhang, Weinan E
2018 arXiv   pre-print
We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schr\"odinger equation.  ...  This opens up new possibilities for solving large-scale many-electron Schr\"odinger equation.  ...  However, there have been few attempts to solve the many-electron Schrödinger equations based on DNN, and this constitutes the main objective of this work.  ... 
arXiv:1807.07014v3 fatcat:iqpsgoiezfhaxmtzqix26ayfny

Machine learning many-electron wave functions via backflow transformations

2020 Journal Club for Condensed Matter Physics  
The goal of determining the electronic structure of molecules and materials by solving the many-body Schrödinger equation has challenged theoretical physics and chemistry over the last century and driven  ...  trial wave functions based on backflow transformations employing neural networks.  ...  The goal of determining the electronic structure of molecules and materials by solving the many-body Schrödinger equation has challenged theoretical physics and chemistry over the last century and driven  ... 
doi:10.36471/jccm_may_2020_01 fatcat:wrfr6xvihvhrzcdemurzxhcrly

Deep learning and the Schrödinger equation

Kyle Mills, Michael Spanner, Isaac Tamblyn
2017 Physical Review A  
We have trained a deep (convolutional) neural network to predict the ground-state energy of an electron in four classes of confining two-dimensional electrostatic potentials.  ...  On randomly generated potentials, for which there is no analytic form for either the potential or the ground-state energy, the neural network model was able to predict the ground-state energy to within  ...  solve the Schrödinger equation, and the need for computing wavefunctions.  ... 
doi:10.1103/physreva.96.042113 fatcat:yvh7o5g3rrbijasrhteq35ehdm

Quantum Ground States from Reinforcement Learning [article]

Ariel Barr, Willem Gispen, Austen Lamacraft
2020 arXiv   pre-print
This provides a variational principle that can be used for reinforcement learning of a neural representation of the drift.  ...  We demonstrate the applicability of our approach to several problems of one-, two-, and many-particle physics.  ...  Acknowledgments We thank Alex Gaunt for useful discussions. We acknowledge support from a National Science Foundation Graduate Research Fellowship under Grant No. DGE-174530 (ARB) and EPSRC Grant No.  ... 
arXiv:2006.09044v1 fatcat:woar6yfrrzhpdbr7tnmuqajc5q

Learning Potentials of Quantum Systems using Deep Neural Networks [article]

Arijit Sehanobish, Hector H. Corzo, Onur Kara, David van Dijk
2021 arXiv   pre-print
Attempts to apply Neural Networks (NN) to a wide range of research problems have been ubiquitous and plentiful in recent literature.  ...  Particularly, the use of deep NNs for understanding complex physical and chemical phenomena has opened a new niche of science where the analysis tools from Machine Learning (ML) are combined with the computational  ...  Most of the deep learning quantum mechanic frameworks introduced so far are focused on either solving the Schrödinger equation or predicting the trends of specific observables such as the system's energy  ... 
arXiv:2006.13297v3 fatcat:fwlanxlz4jbqlouqjeyxzvajgu

Neural Schrödinger Equation: Physical Law as Deep Neural Network

Mitsumasa Nakajima, Kenji Tanaka, Toshikazu Hashimoto
2021 IEEE Transactions on Neural Networks and Learning Systems  
We show a new family of neural networks based on the Schrödinger equation (SE-NET).  ...  In this analogy, the trainable weights of the neural networks correspond to the physical quantities of the Schrödinger equation.  ...  NEURAL SCHRÖDINGER EQUATION In this section, we describe how the Schrödinger equation and its family act as neural networks. A.  ... 
doi:10.1109/tnnls.2021.3120472 pmid:34731081 fatcat:kp3ehoyf3bgmley2fj2kzxyq6y

Predicting Quantum Potentials by Deep Neural Network and Metropolis Sampling [article]

Rui Hong, Peng-Fei Zhou, Bin Xi, Jie Hu, An-Chun Ji, Shi-Ju Ran
2021 arXiv   pre-print
Inspired by quantum potential neural network, we here propose to solve the potential in the Schrodinger equation provided the eigenstate, by combining Metropolis sampling with deep neural network, which  ...  we dub as Metropolis potential neural network (MPNN).  ...  [31] , the authors propose to use a deep neural network named as quantum potential neural network (QPNN) to predict the unknown potential V (r).  ... 
arXiv:2106.03126v2 fatcat:j4dmjdgxerbvdjcz3bevsduv5u

Predicting quantum potentials by deep neural network and metropolis sampling

Rui Hong, Peng-Fei Zhou, Bin Xi, Jie Hu, An-Chun Ji, Shi-Ju Ran
2021 SciPost Physics Core  
Inspired by quantum potential neural network, we here propose to solve the potential in the Schrödinger equation provided the eigenstate, by combining Metropolis sampling with deep neural network, which  ...  we dub as Metropolis potential neural network (MPNN).  ...  [31] , the authors propose to use a deep neural network named as quantum potential neural network (QPNN) to predict the unknown potential V (r).  ... 
doi:10.21468/scipostphyscore.4.3.022 fatcat:3kw2xumdxbawlbted5qreude6q

Approximating Ground State Energies and Wave Functions of Physical Systems with Neural Networks [article]

Cesar Lema, Anna Choromanska
2020 arXiv   pre-print
A neural network realizes a universal trial wave function and is trained in an unsupervised learning framework by optimizing the expectation value of the Hamiltonian of a physical system.  ...  We propose using end-to-end deep learning approach in a variational optimization scheme for approximating the ground state energies and wave functions of these systems.  ...  For the electronic Schrödinger equation, Deep Neural Networks (DNN) integrated into a wave function ansatz was also explored in the VMC setting [12, 13, 8] .  ... 
arXiv:2011.10694v1 fatcat:nmi2yaq6irebdjqtjaob73yuoa

Learning Full Configuration Interaction Electron Correlations with Deep Learning [article]

Hector H. Corzo and Arijit Sehanobish and Onur Kara
2021 arXiv   pre-print
In this report, we present a deep learning framework termed the Electron Correlation Potential Neural Network (eCPNN) that can learn succinct and compact potential functions.  ...  These functions can effectively describe the complex instantaneous spatial correlations among electrons in many--electron atoms.  ...  This approach for defining effective potential functions to describe quantum systems rather than handcrafting solutions for the Schrödinger equation uses a neural network that is developed on the intrinsic  ... 
arXiv:2106.08138v2 fatcat:zaa3pe5bnvaszj4qt742pvie54

A Machine-Learning Method for Time-Dependent Wave Equations over Unbounded Domains [article]

Changjian Xie and Jingrun Chen and Xiantao Li
2021 arXiv   pre-print
For initial conditions lying in the training set, the learned map has good interpolation accuracy, due to the approximation property of deep neural networks.  ...  The accuracy is tested for both the second-order wave equation and the Schrodinger equation, including the nonlinear Schrodinger equation.  ...  The current work aims to solve time-dependent wave equations on unbounded domains using deep learning.  ... 
arXiv:2101.05807v2 fatcat:nfrfnwwqdrbmbppumlvqadem7i

Partial Differential Equations is All You Need for Generating Neural Architectures – A Theory for Physical Artificial Intelligence Systems [article]

Ping Guo, Kaizhu Huang, Zenglin Xu
2021 arXiv   pre-print
network and recurrent neural networks, are generated.  ...  We take finite difference method to discretize NPDE for finding numerical solution, and the basic building blocks of deep neural network architecture, including multi-layer perceptron, convolutional neural  ...  They also applied DNN to solve many-electron schrödinger equation [64] .  ... 
arXiv:2103.08313v1 fatcat:pgfp2k3y3nhzlghybgf2thubxe

Neural network approaches for solving Schrödinger equation in arbitrary quantum wells [article]

Adrian Radu, Carlos A. Duque
2021 arXiv   pre-print
In this work we approach the Schr\"odinger equation in quantum wells with arbitrary potentials, using the machine learning technique.  ...  Two neural networks with different architectures are proposed and trained using a set of potentials, energies, and wave functions previously generated with the classical finite element method.  ...  A problem of very recent interest, mostly for computational material science and quantum chemistry, is solving the Schrödinger equation (SE) using neural models.  ... 
arXiv:2109.03311v1 fatcat:l7slnwtcpnfnbj2uz5ryug7jau

Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach [article]

Jiequn Han, Jianfeng Lu, Mo Zhou
2020 arXiv   pre-print
We propose a new method to solve eigenvalue problems for linear and semilinear second order differential operators in high dimensions based on deep neural networks.  ...  The method shares a similar spirit with diffusion Monte Carlo but augments a direct approximation to the eigenfunction through neural-network ansatz.  ...  Particularly [9, 10, 11, 12] has shown the exciting potential of solving the manyelectron Schrödinger equation with neural networks within the framework of VMC.  ... 
arXiv:2002.02600v2 fatcat:v3kncuqls5bulht7aq6zvsdl7y

Convergence to the fixed-node limit in deep variational Monte Carlo [article]

Zeno Schätzle, Jan Hermann, Frank Noé
2020 arXiv   pre-print
Variational quantum Monte Carlo (QMC) is an ab-initio method for solving the electronic Schrödinger equation that is exact in principle, but limited by the flexibility of the available ansatzes in practice  ...  This analysis helps understanding the superb performance of deep variational ansatzes, and will guide future improvements of the neural network architectures in deep QMC.  ...  INTRODUCTION The fundamental problem in quantum chemistry is to solve the electronic Schrödinger equation as accurately as possible at a manageable cost.  ... 
arXiv:2010.05316v1 fatcat:tt6ln3lvs5eepkhhs5ysgtnzyi
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