Related papers: Structure-preserving integrators for dissipative s…

This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving…

This paper aims to develop a linearly implicit structure-preserving numerical scheme for the space fractional sine-Gordon equation, which is based on the newly developed invariant energy quadratization method. First, we reformulate the…

In this work we introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble. In particular, we consider the equations arising from the so-called density dynamics algorithm with any…

We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral…

We propose a systematic framework for constructing geometric integrators for Hamiltonian systems on Jacobi manifolds. By combining Poissonization of Jacobi structures with homogeneous symplectic bi-realizations, Jacobi dynamics are lifted…

The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…

We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form $H=A+\epsilon B$. We give a constructive proof that for all integer $p$, there exists an integrator with positive steps…

A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…

Studying single-particle dynamics over many periods of oscillations is a well-understood problem solved using symplectic integration. Such integration schemes derive their update sequence from an approximate Hamiltonian, guaranteeing that…

In this paper, we propose a general numerical framework to derive structure-preserving reduced order models for thermodynamically consistent PDEs. Our numerical framework has two primary features: (a) a systematic way to extract reduced…

Dynamic simulation of elastic bodies is a longstanding task in engineering and computer graphics. In graphics, numerical integrators like implicit Euler and BDF2 are preferred due to their stability at large time steps, but they tend to…

We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for the modelling of complex fluids and polymers. The class of methods…

Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…

Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that preserves the global energy. The full-order solutions are…

For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a…

It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…

Recently a new class of numerical integration methods -- ``mixed variable symplectic integrators'' -- has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of…

We perform a numerical analysis of a class of randomly perturbed {H}amiltonian systems and {P}oisson systems. For the considered additive noise perturbation of such systems, we show the long time behavior of the energy and quadratic…

In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…

Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…