Publications related to Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...

Springer International Publishing Ag2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...

2024

Performance and accuracy of cross‐section tracking methods for hydromorphological habitat assessment in wadable rivers with sparse canopy conditions

Giovanni De Cesare, Paolo Perona, Robin Schroff

This article investigates the performance and accuracy of continuous Real-Time Kinematic (RTK) Global Navigation Satellite System (GNSS) position tracking for hydromorphological surveys, based on a comprehensive river restoration monitoring campaign. The a ...

2024

Heuristic Estimation of the Vacuum Energy Density of the Universe: Part II-Analysis Based on Frequency Domain Electromagnetic Radiation

Farhad Rachidi-Haeri, Marcos Rubinstein

In Part I of this paper, an inequality satisfied by the vacuum energy density of the universe was derived using an indirect and heuristic procedure. The derivation is based on a proposed thought experiment, according to which an electron is accelerated to ...

2024

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

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

Alfio Quarteroni, Francesco Regazzoni

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 ...

Elsevier Science Sa2023

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Volkan Cevher, Thomas Michaelsen Pethick, Wanyun Xie

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

2023

Computer-assisted proof of kernel inequalities

Maryna Viazovska, Abhinav Kumar

This data set provides a computer-assisted proof for the kernel inequalities needed to prove universal optimality in the paper "Universal optimality of the E_8 and Leech lattices and interpolation formulas" (by Cohn, Kumar, Miller, Radchenko, and Viazovska ...

EPFL Infoscience2023

An equilibrated flux a posteriori error estimator for defeaturing problems

Annalisa Buffa, Rafael Vazquez Hernandez, Denise Grappein, Ondine Gabrielle Chanon

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

2023

A Shape Derivative Approach to Domain Simplification

Annalisa Buffa, Jochen Peter Hinz, Ondine Gabrielle Chanon, Alessandra Arrigoni

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. ...

Elsevier Sci Ltd2023