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Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…
Monte Carlo techniques have played an important role in understanding strongly-correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum…
Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient relaxation algorithms…
As the demand of real time computing increases day by day, there is a major paradigm shift in processing platform of real time system from single core to multi-core platform which provides advantages like higher throughput, linear power…
We present an adaptive multi-GPU Exchange Monte Carlo method designed for the simulation of the 3D Random Field Model. The algorithm design is based on a two-level parallelization scheme that allows the method to scale its performance in…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
Nowadays the city-wide traffic contains hundreds of thousands of vehicles with different scenarios of their behavior. If a microscopic approach is used it leads to solving tremendous systems of ordinary differential equations whose…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
Nested multi-step stochastic correction offers a possibility to improve updating algorithms for numerical simulations of lattice gauge theories with fermions. The corresponding generalisations of the two-step multi-boson (TSMB) algorithm as…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
The paper discusses multistep nonlinear model-predictive control (NMPC) schemes for the tracking of a car model along a given reference track. In particular we will compare the numerical performance and robustness of classic single step…
It is commonly admitted that non-reversible Markov chain Monte Carlo (MCMC) algorithms usually yield more accurate MCMC estimators than their reversible counterparts. In this note, we show that in addition to their variance reduction…
With the path integral approach, the thermal average in a multi-electronic-state quantum systems can be approximated by the ring polymer representation on an extended configuration space, where the additional degrees of freedom are…
The Circuit Localization track of the Mechanistic Interpretability Benchmark (MIB) evaluates methods for localizing circuits within large language models (LLMs), i.e., subnetworks responsible for specific task behaviors. In this work, we…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…
Maximizing the performance potential of the modern day GPU architecture requires judicious utilization of available parallel resources. Although dramatic reductions can often be obtained through straightforward mappings, further performance…
This paper is devoted to computational algorithms designed to describe the classical Ising magnet in some specific cases when an additional macroscopic restriction in form of constant charge density exists in the system. We developed and…
A quantum Monte Carlo method with non-local update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and…