Related papers: Symplectic algorithm for constant-pressure molecul…
Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
Andersen dynamics is a standard method for molecular simulations, and a precursor of the Hamiltonian Monte Carlo algorithm used in MCMC inference. The stochastic process corresponding to Andersen dynamics is a PDMP (piecewise deterministic…
We propose a novel type of ergostats and thermostats for molecular dynamics simulations. A general class of active particle swarm models is considered, where any specific total energy (alternatively any specific temperature) can be provided…
Almost all Molecular Dynamics (MD) simulations are discrete dynamics with Newton's algorithm first published in 1687, and much later by L. Verlet in 1967. Discrete Newtonian dynamics has the same qualities as Newton's classical analytic…
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…
A recent proposal (see quant-ph/9803068) to simulate semiclassical corrections to classical dynamics by suitable classical stochastic fluctuations is applied to the specific instance of charged beam dynamics in particle accelerators. The…
We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is…
We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state and we approximate the action in a small…
Non-adiabatic molecular dynamics (NAMD) simulations have become an indispensable tool for investigating excited-state dynamics in solids. In this work, we propose a general framework, N$^2$AMD which employs an E(3)-equivariant deep neural…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of…
Sampling from flat energy or density distributions has proven useful in equilibrating complex systems with large energy barriers. Several thermostats and barostats are presented to sample these flat distributions by molecular dynamics.…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…
Various kinds of Ising machines based on unconventional computing have recently been developed for practically important combinatorial optimization. Among them, the machines implementing a heuristic algorithm called simulated bifurcation…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
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 simulate the compression of a two-component Lennard-Jones liquid at a variety of constant temperatures using a molecular dynamics algorithm in an isobaric-isothermal ensemble. The viscosity of the liquid increases with pressure,…
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…