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Concept

Symplectic integrator

Related publications (28)

From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

Fabio Nobile, Thomas Simon Spencer Trigo Trindade

We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potenti ...

Springer Nature Switzerland2025

Applications of the thawed Gaussian approximation to electronic spectroscopy

Eriks Kletnieks

The exploration of electronically excited states and the study of diverse photochemical and photophysical processes are the main goals of molecular electronic spectroscopy. Exact quantum-mechanical simulation of such experiments is, however, beyond current ...

EPFL2024

Estimation of the bar stress based on crack width measurements in reinforced concrete structures

Aurelio Muttoni, Enrique Corres Sojo

Estimating the stress of reinforcing bars and its variations in service conditions can be useful to determine the reserve capacity of structures or to assess the risk of fatigue in the reinforcement. This paper investigates the use crack width measurements ...

Ernst & Sohn2024

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

Euclid: modelling massive neutrinos in cosmology a code comparison

Georges Meylan, Bo Li

The measurement of the absolute neutrino mass scale from cosmological largescale clustering data is one of the key science goals of the Euclid mission. Such a measurement relies on precise modelling of the impact of neutrinos on structure formation, which ...

Iop Publishing Ltd2023

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Giancarlo Ferrari Trecate, Luca Furieri, Liang Xu, Clara Lucía Galimberti

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretiz ...

2023

Efficient geometric integrators for the linear and nonlinear time-dependent Schrödinger equation

Julien Roulet

Many physical and chemical reactions are driven by nonadiabatic processes, which imply the breakdown of the celebrated Born-Oppenheimer approximation. To understand these processes, experimentalists employ spectroscopic techniques. However, the obtained re ...

EPFL2022

A Prony-based approach for accelerating the lightning electromagnetic fields computation above a perfectly conducting ground

Farhad Rachidi-Haeri, Marcos Rubinstein

Lightning strikes can seriously affect the reliability and availability of electrical infrastructures. The computation of lightning-electromagnetic fields represents one of the most crucial steps in the evaluation of the induced effects; thus, having at di ...

Elsevier2022

Geometrical Treatise on the Modelling of 3D Particulate Inclusion-Matrix Microstructures with an Application to Historical Stone Masonry Walls

Mahmoud S. M. Shaqfa

As historical stone masonry structures are vulnerable and prone to damage in earthquakes, investigating their structural integrity is important to reduce injuries and casualties while preserving their historical value. Stone masonry is a composite material ...

EPFL2022

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

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

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

High-order geometric integrators for representation-free Ehrenfest dynamics

Jiri Vanicek, Seonghoon Choi

Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent Schrödinger equa ...

2021

An implicit split-operator algorithm for the nonlinear time-dependent Schrödinger equation

Jiri Vanicek, Julien Roulet

The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schrödinger equations. However, when applied to certain nonlinear time-dependent Schrödinger equations, this algorithm loses time reversibility and seco ...

AIP Publishing2021

Time-reversible and norm-conserving high-order integrators for the nonlinear time-dependent Schrödinger equation: Application to local control theory

Jiri Vanicek, Julien Roulet

The explicit split-operator algorithm has been extensively used for solving not only linear but also nonlinear time-dependent Schrödinger equations. When applied to the nonlinear Gross–Pitaevskii equation, the method remains time-reversible, norm-conservin ...

2021

Analytical Expressions for Lightning Electromagnetic Fields With Arbitrary Channel-Base Current. Part II: Validation and Computational Performance

Farhad Rachidi-Haeri, Marcos Rubinstein

This article provides the implementation procedure, the validation, and some considerations on the computational efforts of the analytical expressions developed for the lightning electromagnetic fields presented in the companion paper. The validation is pr ...

2021

The art of simulating the early universe. Part I. Integration techniques and canonical cases

Daniel Garcia Figueroa, Adrien Florio, Wessel Valkenburg

We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, ...

2021

Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

Jürg Alexander Schiffmann, Patrick Hubert Wagner, Philipp Kaspar Bättig, Wanhui Liu

The nonlinear behavior of a rigid rotor supported by herringbone grooved journal gas bearings (HGJBs) was investigated in this study. The two-dimensional narrow groove theory (2D-NGT) was adopted to model the HGJBs. A set of integrated rotor-bearing state ...

2021

Trust Indicators and Explainable AI: A Study on User Perceptions

Daniel Gatica-Perez, Nicolas Henchoz, Delphine Ribes Lemay, Andreas Sonderegger, Lara Jacqueline Défayes, Thanh Trung Phan, Hélène Michelle Portier

Nowadays, search engines, social media or news aggregators are the preferred services for news access. Aggregation is mostly based on artificial intelligence technologies raising a new challenge: Trust has been ranked as the most important factor for media ...

Springer2021