Ab initio calculation of real solids via neural network ansatz

Abstract

Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose a new architecture that extends molecular neural networks with the inclusion of periodic boundary conditions to enable ab initio calculation of real solids. The accuracy of our approach is demonstrated in four different types of systems, namely the one-dimensional periodic hydrogen chain, the two-dimensional graphene, the three-dimensional lithium hydride crystal, and the homogeneous electron gas, where the obtained results, e.g. total energies, dissociation curves, and cohesive energies, outperform many traditional ab initio methods and reach the level of the most accurate approaches. Moreover, electron densities of typical systems are also calculated to provide physical intuition of various solids. Our method of extending a molecular neural network to periodic systems can be easily integrated into other neural network structures, highlighting a promising future of ab initio solution of more complex solid systems using neural network ansatz, and more generally endorsing the application of machine learning in materials simulation and condensed matter physics.

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• Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas
• Accurate Computation of Quantum Excited States with Neural Networks
• Spin-Dependent Graph Neural Network Potential for Magnetic Materials
• Message-Passing Neural Quantum States for the Homogeneous Electron Gas
• Deep Variational Free Energy Approach to Dense Hydrogen
• PyQMC: an all-Python real-space quantum Monte Carlo module in PySCF
• A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions
• Solving and visualizing fractional quantum Hall wavefunctions with neural network
• Is attention all you need to solve the correlated electron problem?
• Neural Wave Functions for Superfluids
• A framework for efficient ab initio electronic structure with Gaussian Process States
• Taming Landau level mixing in fractional quantum Hall states with deep learning
• Nematic metal in a multi-valley electron gas: Variational Monte Carlo analysis and application to AlAs
• Electric Polarization from Many-Body Neural Network Ansatz
• A deep neural network approach to solve the Dirac equation
• Deep learning quantum Monte Carlo for solids
• DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States
• Quantum Anharmonic Effects in Hydrogen-Bond Symmetrization of High-Pressure Ice
• Quantum Machine Learning of Molecular Energies with Hybrid Quantum-Neural Wavefunction
• Deep variational free energy prediction of dense hydrogen solid at 1200K
• Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions
• Convergence of variational Monte Carlo simulation and scale-invariant pre-training
• Neural Wave Functions for High-Pressure Atomic Hydrogen
• Expressivity of determinantal ansatzes for neural network wave functions