Related papers: A Dimension-adaptive Combination Technique for Unc…

A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of…

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRF) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods,…

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Optimal Control Problems (OCPs) constrained by random partial…

In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged…

We present a novel multiscale numerical approach that combines parallel-in-time computation with hybrid domain adaptation for linear collisional kinetic equations in the diffusive regime. The method addresses the computational challenges of…

Despite impressive performance, deep neural networks require significant memory and computation costs, prohibiting their application in resource-constrained scenarios. Sparse training is one of the most common techniques to reduce these…

We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a…

Axially symmetric processes on spheres, for which the second-order dependency structure may substantially vary with shifts in latitude, are a prominent alternative to model the spatial uncertainty of natural variables located over large…

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method - named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization) - for analyzing high- dimensional data. Unlike in the linear setting where…

Fr\'echet regression has received considerable attention to model metric-space valued responses that are complex and non-Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Fr\'echet…

Real-time path tracing increasingly operates under extremely low sampling budgets, often below one sample per pixel, as rendering complexity, resolution, and frame-rate requirements continue to rise. While super-resolution is widely used in…

Polynomial approximations of computationally intensive models are central to uncertainty quantification. This paper describes an adaptive method for non-intrusive pseudospectral approximation, based on Smolyak's algorithm with generalized…

This paper is dedicated to investigating the adaptive Euler-Maruyama (EM) schemes for the approximation of McKean-Vlasov stochastic differential equations (SDEs) with common noise. When the drift and diffusion coefficients both satisfy the…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce…

Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity)…

Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…

We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…

Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…