相关论文: Variational Monte Carlo for Microscopic Cluster Mo…

We review recent advances in the shell model Monte Carlo approach for the microscopic calculation of statistical and collective properties of nuclei. We discuss applications to the calculation of (i) level densities in nickel isotopes,…

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic…

Neural-network quantum states (NQS) offer a powerful and expressive ansatz for representing quantum many-body wave functions. However, their training via Variational Monte Carlo (VMC) methods remains challenging. It is well known that some…

We introduce a neural network-based approach for modeling wave functions that satisfy Bose-Einstein statistics. Applying this model to small $^4He_N$ clusters (with N ranging from 2 to 14 atoms), we accurately predict ground state energies,…

We revisit the accuracy of the variational Monte Carlo (VMC) method by taking an example of ground state properties for the one-dimensional Hubbard model. We start from the variational wave functions with the Gutzwiller and long-range…

Deep-Learning-based Variational Monte Carlo (DL-VMC) has recently emerged as a highly accurate approach for finding approximate solutions to the many-electron Schr\"odinger equation. Despite its favorable scaling with the number of…

Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…

We present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the ground-state wave function. A memory-efficient version of…

Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous…

Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC…

We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of…

We present a novel quantum Monte Carlo method based on a path integral in Fock space, which allows to compute finite-temperature properties of a many-body nuclear system with a monopole pairing interaction in the canonical ensemble. It…

We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the M{\o}ller-Plesset (MPn) perturbation series, obtaining…

Artificial neural networks have been successfully incorporated into variational Monte Carlo method (VMC) to study quantum many-body systems. However, there have been few systematic studies of exploring quantum many-body physics using deep…

In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable Riemannian manifold. We then combine the notion…

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…

Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…

The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising--like) models in equilibrium statistical mechanics, improving on the mean--field approximation and the Bethe--Peierls approximation,…

We present a variational Monte Carlo (VMC) formulation for the universal equations of state at the Van der Waals length scale [B. Gao, J. Phys. B \textbf{37}, L227 (2004)] for $N$ Bose atoms in a trap. The theory illustrates both how such…