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Potential disagreement in the result induced by discontinuities is revealed in this paper between a novel power system transient simulation scheme using numerical integrators considering second order derivative and conventional ones using…
Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…
We show that symplectic and linearly-implicit integrators proposed by [Zhang and Skeel, 1997] are variational linearizations of Newmark methods. When used in conjunction with penalty methods (i.e., methods that replace constraints by stiff…
In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states,…
The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy of a variational integrator with the order of approximation of the exact discrete Lagrangian by a computable…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…
Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange--Dirac mechanical…
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…
This paper explores the relationship between numerical integrators and optimal control algorithms. Specifically, the performance of the differential dynamical programming (DDP) algorithm is examined when a variational integrator and a newly…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through…
Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach…
A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be…
We propose a fast integrator to a class of dynamical systems with several temporal scales. The proposed method is developed as an extension of the variable step size Heterogeneous Multiscale Method (VSHMM), which is a two-scale integrator…
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…
A nonholonomic system is a mechanical system with velocity constraints not originating from position constraints; rolling without slipping is the typical example. A nonholonomic integrator is a numerical method specifically designed for…
Fractional Pontryagin's systems emerge in the study of a class of fractional optimal control problems but they are not resolvable in most cases. In this paper, we suggest a numerical approach for these fractional systems. Precisely, we…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…