Related papers: Adaptive-Sparse Polynomial Dimensional Decompositi…

This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…

Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…

This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…

In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…

High-dimensional interpolation problems appear in various applications of uncertainty quantification, stochastic optimization and machine learning. Such problems are computationally expensive and request the use of adaptive grid generation…

We propose a scalable method for computing global solutions of nonlinear, high-dimensional dynamic stochastic economic models. First, within a time iteration framework, we approximate economic policy functions using an adaptive,…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…

This paper presents a novel algorithm that leverages Stochastic Gradient Descent strategies in conjunction with Random Features to augment the scalability of Conic Particle Gradient Descent (CPGD) specifically tailored for solving sparse…

The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. In this paper, we study the stochastic collocation methods that can be combined with reduced basis…

Change point detection (CPD) and anomaly detection (AD) are essential techniques in various fields to identify abrupt changes or abnormal data instances. However, existing methods are often constrained to univariate data, face scalability…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

In this work, we propose a new stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Based on the efficiency of the Variable-separation (VS) method in simulating stochastic…

This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…

Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…

Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…

In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multiresolution analysis with directional components. We will do so by constructing subdivision schemes which…

This paper introduces the Parsimonious Dynamic Mode Decomposition (parsDMD), a novel algorithm designed to automatically select an optimally sparse subset of dynamic modes for both spatiotemporal and purely temporal data. By incorporating…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…