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We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions,…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
The entanglement entropy probing novel phases and phase transitions numerically via quantum Monte Carlo has made great achievements in large-scale interacting spin/boson systems. In contrast, the numerical exploration in interacting fermion…
We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent $z$. During a quantum Monte Carlo simulation, the temperature is automatically tuned by the…
We describe time-domain measurements which provide new information about the large-angle nonlinear dynamics of nanomagnets excited by spin-transfer torque from a spin-polarized current. Sampling-oscilloscope measurements, which average over…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…
Wave-function Monte Carlo methods are an important tool for simulating quantum systems, but the standard method cannot be used to simulate decoherence in continuously measured systems. Here we present a new Monte Carlo method for such…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
We present a set of new numerical methods that are relevant to calculating radiation pressure terms in hydrodynamics calculations, with a particular focus on massive star formation. The radiation force is determined from a Monte Carlo…
If a stochastic system during some periods of its evolution can be divided into non-interacting parts, the kinetics of each part can be simulated independently. We show that this can be used in the development of efficient Monte Carlo…
Kinetic descriptions of runaway electrons (RE) are usually based on Fokker-Planck models that determine the probability distribution function (PDF) of RE in 2-dimensional momentum space. Despite of the simplification involved, the…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by…
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
Quantum annealing aims to provide a faster method for finding the minima of complicated functions, compared to classical computing, so there is an increasing interest in the relaxation dynamics of quantum spin systems. Moreover, it is known…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional…
Here we consider the magnetization dynamics in ferromagnetic nanoparticles or films driven by external magnetic field pulses directed transverse to the initial equilibrium state. The excitation pulse drives large-angle ultra-fast…