Some first results on the consistency of spatial regression with partial differential equation regularization

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.

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 ...

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 ...

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 ...

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 ...

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 ...

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, ...

We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...

We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight asymptotic descripti ...

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

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 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 ...

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 ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Reinforcement learning (RL) is inherently rife with non-stationarity since the states and rewards the agent observes during training depend on its changing policy. Therefore, networks in deep RL must be capable of adapting to new observations and fitting n ...

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

Tightly-coupled sensor orientation, i.e. the simultaneous processing of temporal (GNSS and raw inertial) and spatial (image and lidar) constraints in a common adjustment, has demonstrated significant improvement in the quality of attitude determination wit ...

We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potenti ...

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 ...

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

Two -particle Bose-Einstein momentum correlation functions are studied for charged-hadron pairs in lead -lead collisions at a center -of -mass energy per nucleon pair of .'/sNN = 5.02 TeV. The data sample, containing 4.27 x 109 minimum bias events correspo ...

Some first results on the consistency of spatial regression with partial differential equation regularization

Chattez avec Graph Search

Stability: a search for structure

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

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Partial discharge localization in power transformer tanks using machine learning methods

Health Prediction for Lithium-Ion Batteries Under Unseen Working Conditions

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

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

Analysis of Bootstrap and Subsampling in High-dimensional Regularized Regression

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

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

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

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

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

No Representation, No Trust: Connecting Representation, Collapse, and Trust Issues in PPO

On the Generalization of Stochastic Gradient Descent with Momentum

Airborne sensor fusion: Expected accuracy and behavior of a concurrent adjustment

Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

Understanding generalization and robustness in modern deep learning

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Two-particle Bose-Einstein correlations and their Lévy parameters in PbPb collisions at √sNN=5.02 TeV