相关论文: Optimal Linear Interpolation under Differential In…

Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…

Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and…

In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…

We propose a framework for solving partial differential equations (PDEs) motivated by isogeometric analysis (IGA) and local tensor-product splines. Instead of using a global basis for the solution space we use as generators the disjoint…

This paper explores the application of kernel learning methods for parameter prediction and evaluation in the Algebraic Multigrid Method (AMG), focusing on several Partial Differential Equation (PDE) problems. AMG is an efficient iterative…

The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the…

The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It…

In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations…

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…

Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…

Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…

For geospatial modelling and mapping tasks, variants of kriging - the spatial interpolation technique developed by South African mining engineer Danie Krige - have long been regarded as the established geostatistical methods. However,…

We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…

Engineering design involves demanding models encompassing many decision variables and uncontrollable parameters. In addition, unavoidable aleatoric and epistemic uncertainties can be very impactful and add further complexity. The…

Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…