Adaptive reduced basis finite element heterogeneous multiscale method

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This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal decomposition have been ...

We prove a universality result that reduces the free energy of rank-one matrix estimation problems in the setting of mismatched prior and noise to the computation of the free energy for a modified Sherrington–Kirkpatrick spin glass. Our main result is an a ...

Deep learning has shown remarkable potential for industrial applications, particularly in predictive maintenance and condition monitoring. A key challenge in this domain is prognostics, specifically predicting the Remaining Useful Life (RUL) of assets - a ...

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 ...

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 ...

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 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 ...

In the context of discrete choice modeling, the extraction of potential behavioral insights from large datasets is often limited by the poor scalability of maximum likelihood estimation. This paper proposes a simple and fast dataset-reduction method that i ...

In this thesis, we give new protocols that offer a quantum advantage for problems in ML, Physics, and Finance. Quantum mechanics gives predictions that are inconsistent with local realism. The experiment proving this fact (Bell, 1964) gives a quantum proto ...

Dynamical system (DS) based motion planning offers collision-free motion, with closed-loop reactivity thanks to their analytical expression. It ensures that obstacles are not penetrated by reshaping a nominal DS through matrix modulation, which is construc ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

In this paper, we propose an analytical stochastic dynamic programming (SDP) algorithm to address the optimal management problem of price-maker community energy storage. As a price-maker, energy storage smooths price differences, thus decreasing energy arb ...

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 ...

Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model and its variants have been widely used to do so. The historical model conside ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison. Managing their complexity and facilitating their design drove part of the co-evolution of mode ...

Activity-based models offer the potential for a far deeper understanding of daily mobility behaviour than trip-based models. Based on the fundamental assumption that travel demand is derived from the need to do activities, they are flexible tools that aim ...

How to measure students' Computational Problem-Solving (CPS) competencies is an ongoing research topic. Prevalent approaches vary by measurement tools (e.g., interactive programming, multiple-choice tests, or programming-independent tests) and task types ( ...

Adaptive reduced basis finite element heterogeneous multiscale method

Chattez avec Graph Search

Deflation-based certified greedy algorithm and adaptivity for bifurcating nonlinear PDEs

Estimating Rank-One Matrices with Mismatched Prior and Noise: Universality and Large Deviations

Overcoming Distribution Shifts and Imbalance Challenges in Representation Learning for Deep Regression Models

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Spectral Estimators for High-Dimensional Matrix Inference

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

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

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

Resampling estimation of discrete choice models

Quantum Protocols for ML, Physics, and Finance

Reactive collision-free motion generation in joint space via dynamical systems and sampling-based MPC

Reliable data-driven decision-making through optimal transport

Energy Management of Price-Maker Community Energy Storage by Stochastic Dynamic Programming

Stability: a search for structure

Generalized Bradley-Terry Models for Score Estimation from Paired Comparisons

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

Graph generative deep learning models with an application to circuit topologies

OASIS: An integrated optimisation framework for activity scheduling

A Comparative Analysis of Tools & Task Types for Measuring Computational Problem-Solving