相关论文: Monte Carlo PDE Solvers for Nonlinear Radiative Bo…

We present Arepo-MCRT, a novel Monte Carlo radiative transfer (MCRT) radiation-hydrodynamics (RHD) solver for the unstructured moving-mesh code Arepo. Our method is designed for general multiple scattering problems in both optically thin…

The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here, we employ the recently developed \textit{ab initio} permutation blocking path integral Monte Carlo (PB-PIMC) technique…

Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…

The results of analytical approximations and extensive calculations based on a path integral Monte Carlo (PIMC) scheme are presented. A new (direct) PIMC method allows for a correct determination of thermodynamic properties such as energy…

This paper is devoted to the study of a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the…

This paper studies the PML method for wave scattering in a half space of homogeneous medium bounded by a two-dimensional, perfectly conducting, and locally defected periodic surface, and develops a high-accuracy boundary-integral-equation…

The claim that Monte Carlo is the most accurate method is a case of misattributed credit. This claim is based on experience with advanced systems MCNPX, Geant4 and EGS. These systems achieve remarkable performance because they use most…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…

Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural…

We apply the Monte Carlo method to solving the Dirichlet problem of linear parabolic equations with fractional Laplacian. This method exploit- s the idea of weak approximation of related stochastic differential equations driven by the…

Recent advances in differentiable rendering have enabled high-quality reconstruction of 3D scenes from multi-view images. Most methods rely on simple rendering algorithms: pre-filtered direct lighting or learned representations of…

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…

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 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…

We propose a method of simulation that is based on the averaging of formal solutions of the transfer equation by taking the integral by the Monte Carlo method. This method is used to compute two models, which correspond to the limiting…

The numerically exact path integral Monte Carlo approach for the real-time evolution of dissipative quantum systems (PIMC), particularly suited for systems with discrete configuration space (tight-binding systems), is extended to treat…

We discuss multivariate Monte Carlo methods appropriate for X-ray dispersive spectrometers. Dispersive spectrometers have many advantages for high resolution spectroscopy in the X-ray band. Analysis of data from these instruments is…

We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…

We describe a variant of the dressing method giving alternative representation of multidimensional nonlinear PDE as a system of Integro-Differential Equations (IDEs) for spectral and dressing functions. In particular, it becomes single…