相关论文: IGA-based Multi-Index Stochastic Collocation for r…

Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via…

We use generalized Gaussian quadratures for exponentials to develop a new ODE solver. Nodes and weights of these quadratures are computed for a given bandlimit $c$ and user selected accuracy $\epsilon$, so that they integrate functions…

A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational…

Subsea umbilical and power cables contain a large number of contact interfaces between different geometries and materials. These complex interactions rise significant challenges for accurately considering contact surface properties by using…

We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…

Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…

In SLAM (Simultaneous localization and mapping) problems, Pose Graph Optimization (PGO) is a technique to refine an initial estimate of a set of poses (positions and orientations) from a set of pairwise relative measurements. The…

In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation…

Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…

We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences.…

We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the…

Recent work has extended the invariance principle for out-of-distribution (OOD) generalization from Euclidean to graph data, where challenges arise due to complex structures and diverse distribution shifts in node attributes and topology.…

Since Estimation of Distribution Algorithms (EDA) were proposed, many attempts have been made to improve EDAs' performance in the context of global optimization. So far, the studies or applications of multivariate probabilistic model based…

The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary…

We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses…

This paper presents a new stochastic preconditioning approach. For symmetric diagonally-dominant M-matrices, we prove that an incomplete LDL factorization can be obtained from random walks, and used as a preconditioner for an iterative…

\texttt{DiscoTEX} is a highly accurate numerical algorithm for computing numerical weak-form solutions to distributionally sourced partial differential equations (PDE)s. The aim of this second paper, succeeding \cite{da2024discotex}, is to…

Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…

Coupled partial differential equations underpin a wide range of multiphysics systems, yet existing neural PDE solvers still struggle to resolve localized high-risk regions and often fail to preserve structural admissibility across coupled…

In this work, we combine the idea of data-driven polynomial chaos expansions with the weighted least-square approach to solve uncertainty quantification (UQ) problems. The idea of data-driven polynomial chaos is to use statistical moments…