Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs

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The unifying theme of this thesis are decision trees. Given a boolean function

f

and an input

x

, a decision tree computes the value

f(x)

by repeatedly querying bits of

x

. Our work is two-fold. On one hand, we investigate direct sums and other relat ...

In recent years, there has been a surge of interest in predicting computed activation barriers, to enable the acceleration of the automated exploration of reaction networks. Consequently, various predictive approaches have emerged, ranging from graph-based ...

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our mod ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...

We investigate the mechanics of bistable, hard-magnetic, elastic beams, combining experiments, finite-element modelling (FEM) and a reduced-order theory. The beam is made of a hard magneto-rheological elastomer, comprising two segments with antiparallel ma ...

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Digital brain atlases define a hierarchy of brain regions and their locations in three-dimensional space. They provide a standard coordinate system in which diverse datasets can be integrated for visualization and analysis. They also enable building of dat ...

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vond.rejc et al. (2014) [24] beyond the Fourier basis. In particular, we ...

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. But depen ...

The conjugate heat transfer in mixtures of a fluid and single granular clusters is studied in this paper using a novel lattice Boltzmann method (LBM) programmed for parallel computation on the graphics processing unit (GPU). The LBM is validated for heat c ...

The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques ind ...

In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...

The alkali-silica reaction (ASR), also known as concrete cancer, is one of the most prevalent causes of concrete degradation. In this chemical reaction, amorphous silica in the aggregates reacts with alkalis in the pore solution. By absorbing water, hydrop ...

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs

Chattez avec Graph Search

The Power of Decision Trees for Composition and Search Problems

Benchmarking machine-readable vectors of chemical reactions on computed activation barriers

Positive Definite Completions and Continuous Graphical Models

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

On a Finite-Size Neuronal Population Equation

Analysis-aware defeaturing of complex geometries with Neumann features

Snap buckling of bistable beams under combined mechanical and magnetic loading

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Enhancement of brain atlases with region-specific coordinate systems: flatmaps and barrel column annotations

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Analysis-aware defeaturing of complex geometries

Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

Adaptive analysis-aware defeaturing

Conjugate heat transfer in isolated granular clusters with interstitial fluid using lattice Boltzmann method

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Structure-preserving approaches and data-driven closure modeling for model order reduction

Efficient Meso-Scale Modeling of Alkali-Silica-Reaction Damage in Concrete

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution