Nonideal Sampling and Regularization Theory

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Outer space sustainability is rapidly becoming a major focal area in global politics. Amidst governance challenges ranging from orbital debris over atmospheric pollution up to space resource exploration, policymakers, academics, industry, and civil society ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

Battery health prediction is significant while challenging for intelligent battery management. This article proposes a general framework for both short-term and long-term predictions of battery health under unseen dynamic loading and temperature conditions ...

This paper presents a comparison of machine learning (ML) methods used for three-dimensional localization of partial discharges (PD) in a power transformer tank. The study examines ML and deep learning (DL) methods, ranging from support vector machines (SV ...

Dynamic downscaling of atmospheric forcing data to the hectometer resolution has shown increases in accuracy for landsurface models, but at great computational cost. Here we present a validation of a novel intermediate complexity atmospheric model, HICAR, ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly w ...

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

We describe a novel method to compute the components of dynamo tensors from direct magnetohydrodynamic (MHD) simulations. Our method relies upon an extension and generalization of the standard H & ouml;gbom CLEAN algorithm widely used in radio astronomy to ...

In this thesis, we study two closely related directions: robustness and generalization in modern deep learning. Deep learning models based on empirical risk minimization are known to be often non-robust to small, worst-case perturbations known as adversari ...

Surrogate-based optimization is widely used for aerodynamic shape optimization, and its effectiveness depends on representative sampling of the design space. However, traditional sampling methods are hard-pressed to effectively sample high-dimensional desi ...

Herein, machine learning (ML) models using multiple linear regression (MLR), support vector regression (SVR), random forest (RF) and artificial neural network (ANN) are developed and compared to predict the output features viz. specific capacitance (Csp), ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

We investigate the distributional extension of the k-plane transform in Rd and of related operators. We parameterize the k-plane domain as the Cartesian product of the Stiefel manifold of orthonormal k-frames in Rd with Rd-k. This parameterization imposes ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...

Nonideal Sampling and Regularization Theory

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Workshop Outcomes Summary Paper - Space Sustainability: Bridging Initiatives and Perspectives

Spectral Estimators for High-Dimensional Matrix Inference

Health Prediction for Lithium-Ion Batteries Under Unseen Working Conditions

Partial discharge localization in power transformer tanks using machine learning methods

Intermediate complexity atmospheric modeling in complex terrain: is it right?

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Towards Trustworthy Deep Learning for Image Reconstruction

Efficient local linearity regularization to overcome catastrophic overfitting

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Iterative removal of sources to model the turbulent electromotive force

Understanding generalization and robustness in modern deep learning

DiffAirfoil: An Efficient Novel Airfoil Sampler Based on Latent Space Diffusion Model for Aerodynamic Shape Optimization

Machine learning models for prediction of electrochemical properties in supercapacitor electrodes using MXene and graphene nanoplatelets

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

DISTRIBUTIONAL EXTENSION AND INVERTIBILITY OF THE k-PLANE TRANSFORM AND ITS DUAL

Stability: a search for structure

Exploiting the Signal-Leak Bias in Diffusion Models