Related papers: Sensitivity-driven adaptive sparse stochastic appr…
The bootstrap algebraic multigrid framework allows for the adaptive construction of algebraic multigrid methods in situations where geometric multigrid methods are not known or not available at all. While there has been some work on…
This paper presents an efficient surrogate modeling strategy for the uncertainty quantification and Bayesian calibration of a hydrological model. In particular, a process-based dynamical urban drainage simulator that predicts the discharge…
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…
Simultaneous sparse approximation (SSA) seeks to represent a set of dependent signals using sparse vectors with identical supports. The SSA model has been used in various signal and image processing applications involving multiple…
Global sensitivity metrics are essential tools for assessing parameter importance in complex models, particularly when precise information about parameter values is unavailable. In many cases, such metrics are used to provide parameter…
The proximal stochastic gradient method (PSGD) is one of the state-of-the-art approaches for stochastic composite-type problems. In contrast to its deterministic counterpart, PSGD has been found to have difficulties with the correct…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
In this work, we propose a novel adaptive grid mapping approach, the Adaptive Patched Grid Map, which enables a situational aware grid based perception for autonomous vehicles. Its structure allows a flexible representation of the…
The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be used for approximating high-dimensional functions and, in particular, for surrogate-model-based uncertainty quantification. It is lightweight,…
We consider the stabilization of Vlasov--Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy…
Fully finetuning foundation language models (LMs) with billions of parameters is often impractical due to high computational costs, memory requirements, and the risk of overfitting. Although methods like low-rank adapters help address these…
The accuracy of Lagrangian point-particle models for simulation of particle-laden flows may degrade when the particle and fluid momentum equations are two-way coupled. In these cases the fluid velocity at the location of the particle, which…
The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic…
Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a…
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 tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
The growing integration of renewable energy sources has significantly reduced grid inertia, making modern power systems more vulnerable to instabilities. Accurate estimation of dynamic parameters such as inertia constants and damping…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…