Related papers: Voronoi integration of the rendering equation
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
Monte Carlo simulations are a crucial tool for the analysis and prediction of various background components in liquid xenon (LXe) detectors. With improving shielding in new experiments, the simulation of external backgrounds, such as…
Hierarchical models represent a challenging setting for inference algorithms. MCMC methods struggle to scale to large models with many local variables and observations, and variational inference (VI) may fail to provide accurate…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…
A general synthetic iterative scheme is proposed to solve the Enskog equation within a Monte Carlo framework. The method demonstrates rapid convergence by reducing intermediate Monte Carlo evolution and preserves the asymptotic-preserving…
This paper presents an algorithm to obtain an event-based video from noisy frames given by physics-based Monte Carlo path tracing over a synthetic 3D scene. Given the nature of dynamic vision sensor (DVS), rendering event-based video can be…
Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
Reconstruction of one-dimensional kinematic distributions from calculations based on high-dimensional Monte-Carlo integration is a standard problem in high-energy physics. Traditionally, this is done by collecting randomly-generated events…
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…
In the Large Language Model(LLM) reasoning scenario, people often estimate state value via Monte Carlo sampling. Though Monte Carlo estimation is an elegant method with less inductive bias, noise and errors are inevitably introduced due to…
We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand,…
Monte Carlo simulations of neutronic systems are computationally intensive and demand significant memory resources for high-fidelity modeling. Compressed sensing enables accurate reconstruction of signals from significantly fewer samples…
The point inclusion tests for polygons, in other words the point-in-polygon (PIP) algorithms, are fundamental tools for many scientific fields related to computational geometry, and they have been studied for a long time. The PIP algorithms…