Solving many-electron Schrödinger equation using deep neural networks

@article{Han2019SolvingMS,
  title={Solving many-electron Schr{\"o}dinger equation using deep neural networks},
  author={Jiequn Han and Linfeng Zhang and E Weinan},
  journal={J. Comput. Phys.},
  year={2019},
  volume={399}
}

Figures and Tables from this paper

Neural network approaches for solving Schrödinger equation in arbitrary quantum wells
TLDR
In this work, 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 to approach the Schrödinger equation in quantum wells with arbitrary potentials using the machine learning technique.
Predicting Quantum Potentials by Deep Neural Network and Metropolis Sampling
TLDR
A loss function is proposed to explicitly involve the energy in the optimization for its accurate evaluation of Metropolis potential neural network (MPNN), which shows excellent accuracy and stability on predicting not just the potential to satisfy the Schrödinger equation, but also the eigen-energy.
Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks
TLDR
This work restricts the optimization process such that up to 95 percent of weights in a neural network model are in fact equal across varying molecular geometries, which opens a promising route towards pre-trained neural network wavefunctions that yield high accuracy even across different molecules.
Approximating Ground State Energies and Wave Functions of Physical Systems with Neural Networks
TLDR
It is demonstrated that the proposed end-to-end deep learning approach obtains approximations of ground state energies and wave functions that are highly accurate, which makes it a potentially plausible candidate for solving more complex physical systems for which analytical solutions are beyond reach.
Weakly-supervised learning on Schrodinger equation
We propose a machine learning method to solve Schrödinger equations for a Hamiltonian that consists of an unperturbed Hamiltonian and a perturbation. We focus on the cases where the unperturbed
Fermionic neural network with effective core potential
TLDR
This work integrates a powerful neural-network based model (FermiNet) with the effective core potential method, which helps to reduce the complexity of the problem by replacing inner core electrons with additional semi-local potential terms in Hamiltonian.
Towards the ground state of molecules via diffusion Monte Carlo on neural networks
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant devel-opments in the past decades and become one of the go-to methods when accurate ground state energy of molecules
Functional tensor network solving many-body Schrödinger equation 
TLDR
The functional tensor network (FTN) approach to solve the many-body Schrödinger equation is proposed, and can be used as a general solver of the differential equations with many variables.
Vandermonde Wave Function Ansatz for Improved Variational Monte Carlo
TLDR
It is observed that while the use of neural networks in VMC can result in highly accurate solutions, further work is necessary to determine an appropriate balance between computational time and accuracy.
Gold-standard solutions to the Schr\"odinger equation using deep learning: How much physics do we need?
TLDR
A novel deep learning architecture is introduced that achieves 40-70% lower energy error at 8x lower computational cost compared to previous approaches and establishes a new benchmark by calculating the most accurate variational ground state energies ever published for a number of different atoms and molecules.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 120 REFERENCES
Alleviation of the Fermion-sign problem by optimization of many-body wave functions
We present a simple, robust, and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice
Approximating quantum many-body wave functions using artificial neural networks
In this paper, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers
Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep
Solving the Bose–Hubbard Model with Machine Learning
Motivated by the recent successful application of artificial neural networks to quantum many-body problems [G. Carleo and M. Troyer, Science 355, 602 (2017)], a method to calculate the ground state
Quantum Monte Carlo method using phase-free random walks with slater determinants.
TLDR
A quantum Monte Carlo method for many fermions using random walks in the space of Slater determinants is developed, and the calculated binding energies of dimers and cohesive energy of bulk Si are comparable to the best existing theoretical results.
Quantum Monte Carlo simulations of solids
This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic
Method to Solve Quantum Few-Body Problems with Artificial Neural Networks
  • H. Saito
  • Physics, Computer Science
    Journal of the Physical Society of Japan
  • 2018
TLDR
A machine learning technique to obtain the ground states of quantum few-body systems using artificial neural networks is developed and is applied to the Calogero-Sutherland model in one-dimensional space and Efimov bound states in three- dimensional space.
Solving the quantum many-body problem with artificial neural networks
TLDR
A variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons and a reinforcement-learning scheme that is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems.
Generalized neural-network representation of high-dimensional potential-energy surfaces.
TLDR
A new kind of neural-network representation of DFT potential-energy surfaces is introduced, which provides the energy and forces as a function of all atomic positions in systems of arbitrary size and is several orders of magnitude faster than DFT.
Deep Potential: a general representation of a many-body potential energy surface
TLDR
Deep Potential is able to reproduce the original model, whether empirical or quantum mechanics based, within chemical accuracy, and the computational cost of this new model is not substantially larger than that of empirical force fields.
...
1
2
3
4
5
...