Machine Learning Wavefunction

Abstract

This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object, and models thereof require enough flexibility to properly describe the complex interactions between the particles, but at the same time a sufficiently compact representation to be useful in practice. Machine learning techniques offer an ideal mathematical framework to satisfy these requirements, and provide algorithms for their optimization in both supervised and unsupervised fashions. In this chapter, various examples of machine learning wavefunctions are presented and their strengths and weaknesses with respect to traditional quantum chemical approaches are discussed; first in theory, and then in practice with two case studies.

arXiv commentTo be published in the upcoming book "Quantum Chemistry in the Age of Machine Learning", edited by P. Dral

References in corpus (40)

• SchNet - a deep learning architecture for molecules and materials
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantum-Chemical Insights from Deep Tensor Neural Networks
• Tensor networks for complex quantum systems
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Quantum Entanglement in Neural Network States
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• A Transferable Machine-Learning Model of the Electron Density
• Recurrent Neural Network Wave Functions
• Symmetries and many-body excited states with neural-network quantum states
• Fermionic neural-network states for ab-initio electronic structure
• Equivalence of restricted Boltzmann machines and tensor network states
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
• Approximating quantum many-body wave-functions using artificial neural networks
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• Artificial Neural Network Methods in Quantum Mechanics
• Constructing exact representations of quantum many-body systems with deep neural networks
• Quantum Machine Learning for Electronic Structure Calculations
• Approximating strongly correlated spin and fermion wavefunctions with correlator product states
• Machine Learning Configuration Interaction
• Solving frustrated quantum many-particle models with convolutional neural networks
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Neural network wave functions and the sign problem
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Neural network representation of tensor network and chiral states
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• A deep neural network for molecular wave functions in quasi-atomic minimal basis representation
• Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks
• Determinant-free fermionic wave function using feed-forward neural networks
• Convergence to the fixed-node limit in deep variational Monte Carlo
• Gaussian Process States: A data-driven representation of quantum many-body physics
• Boltzmann machines as two-dimensional tensor networks
• On Representing (Anti)Symmetric Functions
• A Bayesian Inference Framework for Compression and Prediction of Quantum States
• Introduction to the variational and diffusion Monte Carlo methods

Cited by in corpus (1)

• Ab-initio quantum chemistry with neural-network wavefunctions