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We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
A simple and stable method for computing accurate expectation values of observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual ``bare'' estimator…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model in order to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater…
Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…
Constructing more expressive ansatz has been a primary focus for quantum Monte Carlo, aimed at more accurate \textit{ab initio} calculations. However, with more powerful ansatz, e.g. various recent developed models based on neural-network…
We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying…
In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate…
Partial differential equations (PDEs) with spatially-varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional PDE solvers struggle with the immense complexity found in…
We use variational quantum Monte Carlo to calculate the density-functional exchange-correlation hole n_{xc}, the exchange-correlation energy density e_{xc}, and the total exchange-correlation energy E_{xc}, of several electron gas systems…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
The computation of free energies is a common issue in statistical physics. A natural technique to compute such high dimensional integrals is to resort to Monte Carlo simulations. However these techniques generally suffer from a high…
We propose a new variational Monte Carlo (VMC) method with an energy variance extrapolation for large-scale shell-model calculations. This variational Monte Carlo is a stochastic optimization method with a projected correlated condensed…
The dynamics of samples in the continuous-imaginary-time quantum world-line Monte Carlo simulations with extended ensembles are investigated. In the case of a conventional flat ensemble on the one-dimensional quantum S=1 bi-quadratic model,…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
An appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the various methods for the 1D Heisenberg ring…
Obtaining accurate solutions to the Schr\"odinger equation is the key challenge in computational quantum chemistry. Deep-learning-based Variational Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms of accuracy,…
We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we…
Fixed-node diffusion Monte Carlo (FNDMC) is a stochastic quantum many-body method that has a great potential in electronic structure theory. We examine how FNDMC satisfies exact constraints, linearity and derivative discontinuity of total…