Publications associées à Linearization and Identification of Multiple-Attractor Dynamical Systems through Laplacian Eigenmaps

Random matrix methods for high-dimensional machine learning models

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

EPFL2024

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

Aude Billard, Nadia Barbara Figueroa Fernandez, Mikhail Koptev

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 ...

Sage Publications Ltd2024

Interpret3C: Interpretable Student Clustering Through Individualized Feature Selection

Julian Thomas Blackwell, Tanja Christina Käser Jacober, Paola Mejia Domenzain, Vinitra Swamy, Isadora Alves de Salles

Clustering in education, particularly in large-scale online environments like MOOCs, is essential for understanding and adapting to diverse student needs. However, the effectiveness of clustering depends on its interpretability, which becomes challenging w ...

2024

Topics in statistical physics of high-dimensional machine learning

Hugo Chao Cui

In the past few years, Machine Learning (ML) techniques have ushered in a paradigm shift, allowing the harnessing of ever more abundant sources of data to automate complex tasks. The technical workhorse behind these important breakthroughs arguably lies in ...

EPFL2024

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Nature Portfolio2024

Few-shot Learning for Efficient and Effective Machine Learning Model Adaptation

Arnout Jan J Devos

Machine learning (ML) enables artificial intelligent (AI) agents to learn autonomously from data obtained from their environment to perform tasks. Modern ML systems have proven to be extremely effective, reaching or even exceeding human intelligence. Altho ...

EPFL2024

Towards Trustworthy Deep Learning for Image Reconstruction

Alexis Marie Frederic Goujon

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

Stability: a search for structure

Wouter Jongeneel

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 ...

EPFL2024

Robust machine learning for neuroscientific inference

Steffen Schneider

Modern neuroscience research is generating increasingly large datasets, from recording thousands of neurons over long timescales to behavioral recordings of animals spanning weeks, months, or even years. Despite a great variety in recording setups and expe ...

EPFL2024

Partial discharge localization in power transformer tanks using machine learning methods

Farhad Rachidi-Haeri, Marcos Rubinstein, Hamidreza Karami

This paper presents a comparison of machine learning (ML) methods used for three-dimensional localization of partial discharges (PD) in a power transformer tank. The study examines ML and deep learning (DL) methods, ranging from support vector machines (SV ...

Nature Publishing Group2024

Dynamical system approach to navigation around obstacles

Aude Billard, Aradhana Nayak

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...

2024

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

Alireza Karimi, Mert Eyuboglu

This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...

2024

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

Searching for the Thinnest Metallic Wire

Nicola Marzari, Davide Campi

One-dimensional materials have gained much attention in the last decades: from carbon nanotubes to ultrathin nanowires to few-atom atomic chains, these can all display unique electronic properties and great potential for next-generation applications. Exfol ...

Amer Chemical Soc2024

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Volkan Cevher, Fanghui Liu

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...

2024

Social Opinion Formation and Decision Making Under Communication Trends

Ali H. Sayed, Virginia Bordignon, Mert Kayaalp

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We stud ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Unlabeled Principal Component Analysis and Matrix Completion

Liangzu Peng, Yunzhen Yao

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

Microtome Publishing2024

Aggregating Spatial and Photometric Context for Photometric Stereo

David Honzátko

Photometric stereo, a computer vision technique for estimating the 3D shape of objects through images captured under varying illumination conditions, has been a topic of research for nearly four decades. In its general formulation, photometric stereo is an ...

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

Frustrated magnets in the limit of infinite dimensions: Dynamics and disorder-free glass transition

Achille Mauri

We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...

Amer Physical Soc2024