Related papers: High order symplectic integrators for planetary dy…
Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in…
Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…
In this paper, we introduces a Pseudo-Symplectic Neural Network (PSNN) for learning general Hamiltonian systems (both separable and non-separable) from data. To address the limitations of existing structure-preserving methods (e.g.,…
We present a reversible and symplectic algorithm called ROLL, for integrating the equations of motion in molecular dynamics simulations of simple fluids on a hypersphere $\mathcal{S}^d$ of arbitrary dimension $d$. It is derived in the…
The reproducibility of experiments is one of the main principles of the scientific method. However, numerical N-body experiments, especially those of planetary systems, are currently not reproducible. In the most optimistic scenario, they…
We present IAS15, a 15th-order integrator to simulate gravitational dynamics. The integrator is based on a Gau\ss-Radau quadrature and can handle conservative as well as non-conservative forces. We develop a step-size control that can…
We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point…
Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a "sourrounded" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…
Phase fitting has been extensively used during the last years to improve the behaviour of numerical integrators on oscillatory problems. In this work, the benefits of the phase fitting technique are embedded in discrete Lagrangian…
A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) and Duruisseaux and Leok (2021). It was observed that a careful combination of…
Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy…
We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of…
We investigate the performance of various methods of symplectic integration, which are based on two part splitting of the integration operator, for the numerical integration of multidimensional Hamiltonian systems. We implement these…
We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The…
The polysymplectic analysis of the Short Pulse Equation known in nonlinear optics is used in order to construct a geometric polysymplectic integrator for it. The proposed scheme turns out to be much more effective than other standard…
Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the…
We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…