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We study the application of a quasi-Monte Carlo (QMC) method to a class of semi-linear parabolic reaction-diffusion partial differential equations used to model tumor growth. Mathematical models of tumor growth are largely phenomenological…

Numerical Analysis · Mathematics 2026-02-23 Alexander D. Gilbert , Frances Y. Kuo , Dirk Nuyens , Graham Pash , Ian H. Sloan , Karen E. Willcox

In this paper, we consider a Monte Carlo simulation method (MinMC) that approximates prices and risk measures for a range $\Gamma$ of model parameters at once. The simulation method that we study has recently gained popularity [HS20, FPP22,…

Statistics Theory · Mathematics 2025-10-01 Nils Detering , Nicole Hufnagel , Paul Krühner

Variational Monte Carlo (VMC) is an approach for computing ground-state wavefunctions that has recently become more powerful due to the introduction of neural network-based wavefunction parametrizations. However, efficiently training neural…

Machine Learning · Statistics 2023-10-03 Robert J. Webber , Michael Lindsey

Monte Carlo (MC) simulation includes a wide range of stochastic techniques used to quantitatively evaluate the behavior of complex systems or processes. Microsoft Excel spreadsheets with Visual Basic for Applications (VBA) software is,…

Mathematical Software · Computer Science 2015-07-22 Alexei Botchkarev

The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The…

Computational Physics · Physics 2011-01-28 Jindrich Kolorenc , Lubos Mitas

Conventional diagonalization methods to calculate nuclear energy levels in the framework of the configuration-interaction (CI) shell model approach are prohibited in very large model spaces. The shell model Monte Carlo (SMMC) is a powerful…

Nuclear Theory · Physics 2025-01-08 Y. Alhassid , M. Bonett-Matiz , C. N. Gilbreth , S. Vartak

Computer hardware costs are the limiting factor in producing highly accurate radiation dose calculations on convenient time scales. Because of this, large-scale, full Monte Carlo simulations and other resource intensive algorithms are often…

Medical Physics · Physics 2010-09-28 Roy W. Keyes , Christian Romano , Dorian Arnold , Shuang Luan

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…

Condensed Matter · Physics 2009-10-31 Claudia Filippi , C. J. Umrigar

Monte-Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve particle size distributions from small-angle scattering patterns of dilute solutions of scatterers. The size sensitivity of…

Data Analysis, Statistics and Probability · Physics 2013-03-19 Brian Richard Pauw , Jan-Skov Pedersen , Samuel Tardif , Masaki Takata , Bo Brummersted Iversen

Purpose: To validate the MC-GPU Monte Carlo code for dosimetric studies in x-ray breast imaging modalities: mammography, digital breast tomosynthesis, contrast enhanced digital mammography and breast-CT. Moreover, to implement and validate…

Medical Physics · Physics 2022-04-06 Rodrigo T. Massera , Rowan M. Thomson , Alessandra Tomal

A novel method for simulating the statistical mechanics of molecular systems in which both nuclear and electronic degrees of freedom are treated quantum mechanically is presented. The scheme combines a path integral description of the…

Computational Physics · Physics 2009-10-31 Ruben O. Weht , Jorge Kohanoff , Dario A. Estrin , Charusita Chakravarty

Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or…

Medical Physics · Physics 2022-11-09 Pia Stammer , Lucas Burigo , Oliver Jäkel , Martin Frank , Niklas Wahl

Monte Carlo (MC) simulations are extensively used for various purposes in modern high-energy physics (HEP) experiments. Precision measurements of established Standard Model processes or searches for new physics often require the collection…

Data Analysis, Statistics and Probability · Physics 2022-06-15 Karl Ehataht , Christian Veelken

The advances in materials and biological sciences have necessitated the use of molecular simulations to study polymers. The Markov chain Monte Carlo simulations enable the sampling of relevant microstates of polymeric systems by traversing…

Soft Condensed Matter · Physics 2023-07-24 Monika Angwani , Tushar Mahendrakar , Kaustubh Rane

Purpose: Very fast Monte Carlo (MC) simulations of proton transport have been implemented recently on GPUs. However, these usually use simplified models for non-elastic (NE) proton-nucleus interactions. Our primary goal is to build a…

Medical Physics · Physics 2015-06-11 H. Wan Chan Tseung , J. Ma , C. Beltran

Radiative transfer describes the propagation of electromagnetic radiation through an interacting medium. This process is often simulated by the use of the Monte Carlo method, which involves the probabilistic determination and tracking of…

Instrumentation and Methods for Astrophysics · Physics 2020-03-31 A. Krieger , S. Wolf

We have previously described RapidBrachyMCTPS, a brachytherapy treatment planning toolkit consisting of a graphical user interface (GUI) and a Geant4-based Monte Carlo (MC) dose calculation engine. This work describes the tools that have…

Medical Physics · Physics 2020-07-07 Harry Glickman , Majd Antaki , Christopher Deufel , Shirin A. Enger

Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the…

Statistical Mechanics · Physics 2009-11-07 A. van de Walle , M. Asta

Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions.…

Computation · Statistics 2026-04-07 Arghya Mukherjee , Dootika Vats

We propose a new variational Monte Carlo (VMC) approach based on the Krylov subspace for large-scale shell-model calculations. A random walker in the VMC is formulated with the $M$-scheme representation, and samples a small number of…

Nuclear Theory · Physics 2015-06-15 Noritaka Shimizu , Takahiro Mizusaki , Kazunari Kaneko