We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for separable Hamiltonian systems with quadratic kinetic energy may be particularly useful when applied to Hamiltonian systems where an evaluation of the Hessian is significantly more expensive than an evaluation of its gradient, e.g. in molecular dynamics simulations of classical systems. Numerical experiments of an N-body problem, as well as applications to the molecular dynamics step in the Hybrid Monte Carlo (HMC) algorithm for lattice simulations of the Schwinger model and Quantum Chromodynamics (QCD) verify these expectations.

翻译：我们提出了一种无需基于势能海森矩阵的力梯度项解析表达式的无海森力梯度积分器新框架。由于这类针对具有二次动能的可分离哈密顿系统的新型分解算法，在评估海森矩阵成本远高于评估其梯度的哈密顿系统（例如经典系统的分子动力学模拟）中可能特别有用。通过N体问题的数值实验，以及在施温格模型和量子色动力学(QCD)格点模拟的混合蒙特卡洛(HMC)算法中分子动力学步骤的应用，验证了这些预期。