Related papers: Newton's algorithm for discrete classical dynamics
Molecular Dynamics method is based on solution of Newtonian differential equations of motion. A new very accurate and efficient time-reversible explicit integrator was derived on the basis of second order Tailor expansion of force. There is…
A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are…
We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
The Minkowski operators (addition and substraction of sets in vectorial spaces) has been extensively used for Computer Graphics and Image Processing to represent complex shapes. Here we propose to apply those mathematical concepts to extend…
This paper deals with an implicit Newton-like inertial dynamical system governed by a maximally comonotone inclusion problem in a Hilbert space. Under suitable conditions, we establish not only pointwise estimates and integral estimates for…
We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds…
Molecular dynamics is based on solving Newton's equations for many-particle systems that evolve along complex, highly fluctuating trajectories. The orbital instability and short-time complexity of Newtonian orbits is in sharp contrast to…
We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…
This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers…
In condensed matter physics, particularly in perovskite materials, the rotational motion of molecules and ions is associated with important issues such as ion conduction mechanism. Constrained Molecular Dynamics (MD) simulations offer a…
Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…
Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to…
We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found,…
The Verlet method is still widely used to integrate the equations of motion in ab initio molecular dynamics simulations. We show that the stability limit of the Verlet method may be significantly increased by setting an upper limit on the…
Discrete gradients (DG) or more exactly discrete gradient methods are time integration schemes that are custom-built to preserve first integrals or Lyapunov functions of a given ordinary differential equation (ODE). In conservative…
In this note we approach the classical, Newtonian, gravitational $N$-body problem by mean of a new, original numerical integration method. After a short summary of the fundamental characteristics of the problem, including a sketch of some…
In this paper we will study some interesting properties of modifications of the Euler-Poincar\'e equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism.…
A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…
We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate…