Related papers: Efficient Numerical Schemes for Multidimensional P…

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…

Score-based diffusion models (SBDM) have recently emerged as state-of-the-art approaches for image generation. Existing SBDMs are typically formulated in a finite-dimensional setting, where images are considered as tensors of finite size.…

Motivation: In systems biology, modelling strategies aim to decode how molecular components interact to generate dynamical behaviour. Boolean modelling is more and more used, but the description of the dynamics from two-levels components…

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…

The development of cluster computing frameworks has allowed practitioners to scale out various statistical estimation and machine learning algorithms with minimal programming effort. This is especially true for machine learning problems…

Generating a synthetic population that is both feasible and diverse is crucial for ensuring the validity of downstream activity schedule simulation in activity-based models (ABMs). While deep generative models (DGMs), such as variational…

In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…

With the advancement of diffusion models (DMs) and the substantially increased computational requirements, quantization emerges as a practical solution to obtain compact and efficient low-bit DMs. However, the highly discrete representation…

In this paper, a novel modulation scheme called set partition modulation (SPM) is proposed. In this scheme, set partitioning and ordered subsets in the set partitions are used to form codewords. We define different SPM variants and depict a…

A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…

Meshless methods approximate operators in a specific node as a weighted sum of values in its neighbours. Higher order approximations of derivatives provide more accurate solutions with better convergence characteristics, but they come at…

Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…

This paper describes valuation-based systems for representing and solving discrete optimization problems. In valuation-based systems, we represent information in an optimization problem using variables, sample spaces of variables, a set of…

In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose…

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods…

We formulate a general criterion for the exact preservation of the "lake at rest" solution in general mesh-based and meshless numerical schemes for the strong form of the shallow-water equations with bottom topography. The main idea is a…

The problem of learning a computational model from examples has been receiving growing attention. For the particularly challenging problem of learning models of distributed systems, existing results are restricted to models with a fixed…

In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of the schemes is obtained by adding to the mass balance…

Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…