Publications related to Mathematical physics

Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain

Human babies have a natural desire to interact with new toys and objects, through which they learn how the world around them works, e.g., that glass shatters when dropped, but a rubber ball does not. When their predictions are proven incorrect, such as whe ...

EPFL2024

Geometric Learning: Leveraging differential geometry for learning and control

Bernardo Fichera

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

EPFL2024

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus

Simon Guilloud

Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe proofs in first-ord ...

2024

Deep Learning Meets Sparse Regularization

Rahul Parhi

Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...

2023

Learning Dynamics of Spring-Mass Models with Physics-Informed Graph Neural Networks

Olga Fink, Vinay Sharma, Manav Manav

We propose a physics-informed message-passing graph neural network (GNN) for learning the dynamics of springmass systems. The proposed method embeds the underlying physics directly into the message-passing scheme of the GNN. We compare the new scheme with ...

Research Publishing2023

Size dependence of second-harmonic scattering from nanoparticles: Disentangling surface and electrostatic contributions

Sylvie Roke, Arianna Marchioro, Bingxin Chu

Polarimetric angle-resolved second-harmonic scattering (AR-SHS) is an all-optical tool enabling the study of unlabeled interfaces of nano-sized particles in an aqueous solution. As the second harmonic signal is modulated by interference between nonlinear c ...

AIP Publishing2023

Mechanism balancing taxonomy

Simon Nessim Henein, Florent Cosandier, Hubert Pierre-Marie Benoît Schneegans

The balancing of mechanisms consists in distributing their moving masses, inertias, and elastic components in order to achieve key mechanical properties, such as the elimination of the shaking forces and moments exported onto their supporting structure or ...

2023

A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

Annalisa Buffa, Espen Sande, Yannis Dirk Voet

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

2023

Mathematical Foundations of Adaptive Isogeometric Analysis

Annalisa Buffa, Rafael Vazquez Hernandez

This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of ...

SPRINGER2022

High-order accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics

Junming Duan

This paper develops high-order accurate entropy stable (ES) adaptive moving mesh finite difference schemes for the two- and three-dimensional special relativistic hydrodynamic (RHD) and magnetohydrodynamic (RMHD) equations, which is the high-order accurate ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

NATURE PORTFOLIO2022

A taxonomy of surprise definitions

Wulfram Gerstner, Johanni Michael Brea, Alireza Modirshanechi

Surprising events trigger measurable brain activity and influence human behavior by affecting learning, memory, and decision-making. Currently there is, however, no consensus on the definition of surprise. Here we identify 18 mathematical definitions of su ...

2022

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Ketson Roberto Maximiano Dos Santos

A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low-dimensional representation o ...

Wiley2022

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

EPFL2022

Physics-based control of neoclassical tearing modes on TCV

Olivier Sauter, Federico Alberto Alfredo Felici, Cristian Galperti, Mengdi Kong

This paper presents recent progress in studies of neoclassical tearing modes (NTMs) on TCV, concerning the new physics learned and how this physics contributes to a better real-time (RT) control of NTMs. A simple technique that adds a small (sinusoidal) sw ...

IOP Publishing Ltd2022

Structure-Preserving Reduced Basis Methods For Poisson Systems

Jan Sickmann Hesthaven, Cecilia Pagliantini

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

AMER MATHEMATICAL SOC2021

A Statistical Physics approach to a multi-channel Wigner spiked model

Emanuele Mingione, Diego Alberici

In this letter we present a finite temperature approach to a high-dimensional inference problem, the Wigner spiked model, with group-dependent signal-to-noise ratios. For two classes of convex and non-convex network architectures the error in the reconstru ...

IOP Publishing - EPL Association2021

Relaxation of capillary-gravity waves due to contact line nonlinearity: A projection method

François Gallaire, Alessandro Bongarzone, Francesco Viola

We present a physics-inspired mathematical model based on successive linear eigenmode projections to solve the relaxation of small-amplitude and two-dimensional viscous capillary-gravity waves with a phenomenological nonlinear contact line model. We show t ...

American Institute of Physics2021

A Mixed-Integer Linear Programming Formulation for Optimizing Multi-Scale Material and Energy Integration

François Maréchal, Ivan Daniel Kantor, Hür Ebuzer Bütün, Jean-Loup Sylvain Robineau

This research presents a mathematical formulation for optimizing integration of complex industrial systems from the level of unit operations to processes, entire plants, and finally to considering industrial symbiosis opportunities between plants. The fram ...

2020

Sparse coupled logistic regression to estimate co-activation and modulatory influences of brain regions

Dimitri Nestor Alice Van De Ville, Thomas William Arthur Bolton, Ye Tian

Accurate mapping of the functional interactions between remote brain areas with resting-state functional magnetic resonance imaging requires the quantification of their underlying dynamics. In conventional methodological pipelines, a spatial scale of inter ...

IOP PUBLISHING LTD2020