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The Particle-In-Cell (PIC) and Monte Carlo Collisions (MCC) methods are workhorses of many numerical simulations of physical systems. Recently, it was pointed out that, while the two methods can be exactly - or nearly - energy-conserving…

Restricted path integral Monte Carlo simulations have been used to calculate the equilibrium properties of deuterium for two densities: 0.674 and 0.838 gcm^-3 (rs = 2.00 and 1.86) in the temperature range of 10000 < T < 1000000 K. Using the…

This paper proposes several explicit and implicit multistep frequency response optimized integrators considering first or second order derivative. A prediction-based method aiming at accelerating a novel power system transient simulation…

The hybrid Monte Carlo (HMC) algorithm is arguably the most efficient sampling method for general probability distributions of continuous variables. Together with exact Fourier acceleration (EFA) the HMC becomes equivalent to direct…

This study investigates the use of the $J$-integral to compute the statistics of the energy release rate of a random elastic medium. The spatial variability of the elastic modulus is modeled as a homogeneous lognormal random field. Within…

We suggest how to construct an effective low energy Hamiltonian via Monte Carlo starting from a given action. We test it by computing thermodynamical observables like average energy and specific heat for simple quantum systems.

We present a molecular simulation method to simultaneously find multiple transition pathways, and their associated free-energy profiles. The scheme extends path-metadynamics (PMD) [Phys. Rev. Lett. 109, 020601 (2012)] with multiple paths…

Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…

We develop an all-electron path integral Monte Carlo (PIMC) method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend PIMC studies beyond hydrogen and helium to elements with core…

Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…

Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…

This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplicative amount of variance reduction. The proposed meta…

In this paper we explore new ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter.…

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…

Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap…

We present a method for computing free-energy differences using thermodynamic integration with a neural network potential that interpolates between two target Hamiltonians. The interpolation is defined at the sample distribution level, and…

We demonstrate the use of a new algorithm called the Flat Histogram sampling algorithm for the simulation of lattice polymer systems. Thermodynamics properties, such as average energy or entropy and other physical quantities such as…

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…

For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH$_4 $, NH$_3…