The many-body Green's function provides access to electronic properties beyond density-functional theory level in ab inito calculations. In this manuscript, we propose a deep learning framework for predicting the finite-temperature Green's function in atomic orbital space, aiming to achieve a balance between accuracy and efficiency. By predicting the self-energy matrices in Lehmann representation using an equivariant message-passing neural network, our method respects its analytical property and the $E(3)$ equivariance. The Green's function is obtained from the predicted self-energy through the Dyson equation with target total number of electrons. We present proof-of-concept benchmark results for both molecules and simple periodic systems, showing that our method is able to provide an accurate estimate of physical observables such as energy and density of states based on the predicted Green's function.The many-body Green's function provides access to electronic properties beyond density-functional theory level in ab inito calculations. In this manuscript, we propose a deep learning framework for predicting the finite-temperature Green's function in atomic orbital space, aiming to achieve a balance between accuracy and efficiency. By predicting the self-energy matrices in Lehmann representation using an equivariant message-passing neural network, our method respects its analytical property and the $E(3)$ equivariance. The Green's function is obtained from the predicted self-energy through the Dyson equation with target total number of electrons. We present proof-of-concept benchmark results for both molecules and simple periodic systems, showing that our method is able to provide an accurate estimate of physical observables such as energy and density of states based on the predicted Green's function.

arXiv:2312.14680Physical review. B./Physical review. BFeb 6, 202411 citations

DeepQMC: An open-source software suite for variational optimization of deep-learning molecular wave functions

Zeno Schätzle, P. Bernát Szabó, Matěj Mezera +2 more

Computing accurate yet efficient approximations to the solutions of the electronic Schrödinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of development as their core algorithm exhibits a number of favorable properties: it is highly parallel and scales favorably with the considered system size, with an accuracy that is limited only by the choice of the wave function Ansatz. The recently introduced machine-learned parametrizations of quantum Monte Carlo Ansätze rely on the efficiency of neural networks as universal function approximators to achieve state of the art accuracy on a variety of molecular systems. With interest in the field growing rapidly, there is a clear need for easy to use, modular, and extendable software libraries facilitating the development and adoption of this new class of methods. In this contribution, the DeepQMC program package is introduced, in an attempt to provide a common framework for future investigations by unifying many of the currently available deep-learning quantum Monte Carlo architectures. Furthermore, the manuscript provides a brief introduction to the methodology of variational quantum Monte Carlo in real space, highlights some technical challenges of optimizing neural network wave functions, and presents example black-box applications of the program package. We thereby intend to make this novel field accessible to a broader class of practitioners from both the quantum chemistry and the machine learning communities.Computing accurate yet efficient approximations to the solutions of the electronic Schrödinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of development as their core algorithm exhibits a number of favorable properties: it is highly parallel and scales favorably with the considered system size, with an accuracy that is limited only by the choice of the wave function Ansatz. The recently introduced machine-learned parametrizations of quantum Monte Carlo Ansätze rely on the efficiency of neural networks as universal function approximators to achieve state of the art accuracy on a variety of molecular systems. With interest in the field growing rapidly, there is a clear need for easy to use, modular, and extendable software libraries facilitating the development and adoption of this new class of methods. In this contribution, the DeepQMC program package is introduced, in an attempt to provide a common framework for future investigations by unifying many of the currently available deep-learning quantum Monte Carlo architectures. Furthermore, the manuscript provides a brief introduction to the methodology of variational quantum Monte Carlo in real space, highlights some technical challenges of optimizing neural network wave functions, and presents example black-box applications of the program package. We thereby intend to make this novel field accessible to a broader class of practitioners from both the quantum chemistry and the machine learning communities.

The Journal of Chemical PhysicsSep 6, 202325 citations

Machine learning toolbox for quantum many body physics

Filippo Vicentini

Nature Reviews PhysicsJan 29, 20218 citations

Machine Learning for Quantum Many-body Problems

Yusuke Nomura

電子情報通信学会誌Nov 1, 20210 citations

E(3)

equivariance. The Green's function is obtained from the predicted self-energy through the Dyson equation with target total number of electrons. We present proof-of-concept benchmark results for both molecules and simple periodic systems, showing that our method is able to provide an accurate estimate of physical observables such as energy and density of states based on the predicted Green's function.