Concept

Symplectomorphisme

Publications associées (26)

CosmoLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe

Daniel Garcia Figueroa, Adrien Florio, Wessel Valkenburg, Francisco Torrenti

This paper describes CosmoGattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoGattice incorporates a series of features that makes it very versatile and powerful: i) it is ...

ELSEVIER2023

A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape

Berfin Simsek

Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans.The success in practice stems from the ability to successfully train massive neural ...

EPFL2023

Generalised Howe duality and injectivity of induction: the symplectic case

Thomas Gerber

We study the symplectic Howe duality using two new and independent combinatorial methods: via determinantal formulae on the one hand, and via (bi)crystals on the other hand. The first approach allows us to establish a generalised version where weight multi ...

2022

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

Jan Sickmann Hesthaven, Nicolò Ripamonti, Cecilia Pagliantini

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

Einstein's quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism

Fabrizio Minganti

The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbeinlike formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones, rendering th ...

AMER PHYSICAL SOC2022

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Arithmetically rigid schemes via deformation theory of equivariant vector bundles

Maciej Emilian Zdanowicz

We analyze the deformation theory of equivariant vector bundles. In particular, we provide an effective criterion for verifying whether all infinitesimal deformations preserve the equivariant structure. As an application, using rigidity of the Frobenius ho ...

SPRINGER HEIDELBERG2020

Dynamical Reduced Basis Methods for Hamiltonian Systems

Cecilia Pagliantini

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the ric ...

2019

Symplectic Model-Reduction with a Weighted Inner Product

Jan Sickmann Hesthaven, Babak Maboudi Afkham

In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems, symplectic model redu ...

2018

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

Reduced basis methods are popular for approximately solving large and complex systems of dierential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model. Here, we present ...

2017

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