Publications associées à Low rank differential equations for Hamiltonian matrix nearness problems

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

Siam Publications2024

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

Asymmetric phase modulation of light with parity-symmetry broken metasurfaces

Jean-Yves Duboz, Karim Achouri

The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and ...

Optica Publishing Group2023

A mixed precision LOBPCG algorithm

Daniel Kressner, Meiyue Shao, Yuxin Ma

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mix ...

SPRINGER2023

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Daniel Kressner, Ivana Sain Glibic

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Mehmet Fatih Sahin

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

EPFL2023

Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Fabrizio Minganti

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...

AMER PHYSICAL SOC2023

Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation

Cecilia Pagliantini, Jan Sickmann Hesthaven, Nicolò Ripamonti

. High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of para ...

AMER MATHEMATICAL SOC2023

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Cecilia Pagliantini, Jan Sickmann Hesthaven, Nicolò Ripamonti

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the ...

EDP SCIENCES S A2022

Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance

Fabrizio Minganti

The exceptional points (EPs) of non-Hermitian Hamiltonians (NHHs) are spectral degeneracies associated with coalescing eigenvalues and eigenvectors, which are associated with remarkable dynamical properties. These EPs can be generated experimentally in ope ...

AMER PHYSICAL SOC2022

Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data

Matthieu Wyart, Umberto Maria Tomasini, Antonio Sclocchi

Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a 'spectral bias': decomposing the true function f* on the eigenbasis of the ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Systems and methods for energy-efficient measurement of neurophysiological oscillations

Mahsa Shoaran, Uisub Shin

A system for measuring synchrony between two or more regions, or within a single region, of a subject's brain. The system can include a signal conditioning module in communication with a phase extraction module. The signal conditioning module can receive a ...

2022

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

Nicolò Ripamonti

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 ...

EPFL2022

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Yinlin Hu, Wei Wang

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

Second-order adjoint-based sensitivity for hydrodynamic stability and control

Edouard Boujo

Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the most effective, i. ...

Cambridge University Press2021

Scattering Map for the Vlasov–Poisson System

Klaus Martin Widmayer

We construct (modified) scattering operators for the Vlasov–Poisson system in three dimensions, mapping small asymptotic dynamics as t→−∞ to asymptotic dynamics as t→+∞. The main novelty is the construction of modified wave operators, but we also obtain a ...

2023

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Joachim Stubbe, Luigi Provenzano

We present asymptotically sharp inequalities, containing a 2nd term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kroger inequalities in the limit as the eigenvalues tend ...

OXFORD UNIV PRESS2021

Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

2020