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Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel me ...
In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...
The method of moments (MOM), as introduced by R. F. Harrington more than 50 years ago, is reviewed in the context of the classic potential integral equation (PIE) formulations applied to both electrostatic (part 1) and electrodynamic, or full-wave, problem ...
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...
This tutorial covers biomedical image reconstruction, from the foundational concepts of system modeling and direct reconstruction to modern sparsity and learning-based approaches. Imaging is a critical tool in biological research and medicine, and most ima ...
High-resolution schemes for conservation laws need to suitably limit the numerical solution near discontinuities, in order to avoid Gibbs oscillations. The solution quality and the computational cost of such schemes strongly depend on their ability to corr ...
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2023
Optimized Schwarz Methods (OSMs) are based on optimized transmission conditions along the interfaces between the subdomains. Optimized transmission conditions are derived at the theoretical level, using techniques developed in the last decades. The hypothe ...
Springer-Verlag2021
Optical manipulation at the micro- nano-scale is a fascinating topic due to its inherent non-invasive properties and multifaceted applications in various fields such as biology, sensing, micro-fluidics, and micro- nano-robotics. This thesis involves intens ...
EPFL2022
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High fidelity (HF) mathematical models describing the generation of active force in the cardiac muscle tissue typically feature a large number of state variables to capture the intrinsically complex underlying subcellular mechanisms. With the aim of drasti ...
