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Concept

Symplectic geometry

Related publications (25)

RMAML: Riemannian meta-learning with orthogonality constraints

Soumava Kumar Roy

Meta-learning is the core capability that enables intelligent systems to rapidly generalize their prior ex-perience to learn new tasks. In general, the optimization-based methods formalize the meta-learning as a bi-level optimization problem, that is a nes ...

ELSEVIER SCI LTD2023

High-order geometric integrators for the variational Gaussian approximation

Jiri Vanicek, Roya Moghaddasi Fereidani

Among the single-trajectory Gaussian-based methods for solving the time-dependent Schrödinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller’s original thawed Gaussian approximation, it is symplectic, conse ...

2023

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

Daniel Garcia Figueroa, Adrien Florio, Wessel Valkenburg

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

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

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

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

Jan Sickmann Hesthaven, Cecilia Pagliantini, 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

A b-symplectic slice theorem

Anna Kiesenhofer

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...

WILEY2022

Exploring the inner workings of the clove hitch knot

Pedro Miguel Nunes Pereira de Almeida Reis, Tomohiko Sano, Paul Johanns, Paul Grandgeorge

We perform a combined experimental and computational investigation of the clove hitch knot. We develop a physical model for the clove hitch by tying an elastic rod onto a rigid cylinder. In the experiments, we characterize the mechanical performance, geome ...

ELSEVIER2022

Prediction of crack nucleation and propagation in porous ceramics using the phase-field approach

Arata Nakajo

The relevance of the phase-field approach to simulate the fracture in porous ceramics has been investigated. For this purpose, the conditions for the crack initiation using the phase-field model have been compared to the theoretical predictions of the coup ...

ELSEVIER2022

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

Design of Integrally-Attached Timber Plate Structures

Yves Weinand

Design of Integrally-Attached Timber Plate Structures outlines a new design methodology for digitally fabricated spatial timber plate structures, presented with examples from recent construction projects. It proposes an innovative and sustainable design me ...

Routledge, Taylor & Francis Group, London, 20222021

Synthesis of Kit-of-parts Structures for Reuse

Corentin Jean Dominique Fivet, Gennaro Senatore, Jan Friedrich Georg Brütting, Ioannis Mirtsopoulos, Alex-Manuel Muresan

This paper shows a computational workflow to design a kit of parts consisting of linear bars and spherical joints that can be employed to assemble, take apart, and rebuild diverse reticular structures, e.g. gridshells and space frames. Being able to reuse ...

2021

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

Adaptive Gradient Descent without Descent

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Open and Closed Radicals: Local Geometry around Unpaired Electrons Governs Magic-Angle Spinning Dynamic Nuclear Polarization Performance

David Lyndon Emsley, Dominik Józef Kubicki, Gabriele Stevanato, Manuel Cordova, Yu Rao

The development of magic-angle spinning dynamic nuclear polarization (MAS DNP) has allowed atomic-level characterization of materials for which conventional solid-state NMR is impractical due to the lack of sensitivity. The rapid progress of MAS DNP has be ...

2020

Mechanical Characterization of Integrally-Attached Timber Plate Structures: Experimental studies and macro modeling technique

Aryan Rezaei Rad

Spurred by the recent advancements in Computer-Aided Design (CAD), Integral Mechanical Attachment (IMA) technique has been resurrected. Using IMAs, connections between timber elements are established through their form, instead of using additional connecto ...

EPFL2020

A framework to automate the design of digitally-fabricated timber plate structures

Yves Weinand, Petras Vestartas, Aryan Rezaei Rad, Nicolas Henry Pierre Louis Rogeau

The current study uses knowledge from digital architecture, computer science, engineering informatics, and structural engineering to formulate an algorithmic framework for integrated Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) of Integ ...

2021

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 ...

Springer2021

Design optimization of a CFRP-aluminum joint for a bioengineering application

John Botsis, Georgios Pappas

Lightweight design demands and complexity requirements of modern high-end structures in aerospace, automotive, sports and bioengineering can be successfully covered by a combination of fiber reinforced polymers (FRPs) with metallic components. Conventional ...

2019

A Learned Shape-Adaptive Subsurface Scattering Model

Wenzel Alban Jakob, Delio Aleardo Vicini

Subsurface scattering, in which light refracts into a translucent material to interact with its interior, is the dominant mode of light transport in many types of organic materials. Accounting for this phenomenon is thus crucial for visual realism, but exp ...

ASSOC COMPUTING MACHINERY2019