相关论文: Speeding up HMC with better integrators

In this paper, a new class of energy-preserving integrators is proposed and analysed for Poisson systems by using functionally-fitted technology. The integrators exactly preserve energy and have arbitrarily high order. It is shown that the…

We compare the performance of the PHMC algorithm with the one of the HMC algorithm in practical simulations of lattice QCD. We show that the PHMC algorithm can lead to an acceleration of numerical simulations. It is demonstrated that the…

We report on what seems to be an intriguing connection between variable integration time and partial velocity refreshment of Ideal Hamiltonian Monte Carlo samplers, both of which can be used for reducing the dissipative behavior of the…

This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…

There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…

Symplectic integrators are a foundation to the study of dynamical $N$-body phenomena, at scales ranging from from planetary to cosmological. These integrators preserve the Poincar\'e invariants of Hamiltonian dynamics. The $N$-body…

Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…

We use local symplectic Lie groupoids to construct Poisson integrators for generic Poisson structures. More precisely, recursively obtained solutions of a Hamilton-Jacobi-like equation are interpreted as Lagrangian bisections in a…

We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…

By introducing an integration factor to the differential one-form of contact dynamics, equations of motion are derived variationally, and contact Poisson bracket and contact Lagrangian are formulated. Discrete symplectic integrator, named…

Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…

We exhibit a new pre-Lie algebra in the framework of symplectic groupoids and, in turn, introduce a pre-Lie formalism of Butcher trees for the approximation of Hamilton-Jacobi solutions on any symplectic groupoid $\mathcal{G}…

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…

We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete…

We consider how to accelerate fermionic molecular dynamics algorithms by introducing n pseudofermion fields coupled with the nth root of the fermionic kernel. This reduces the maximum pseudofermionic force, and thus allows a larger…

In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It is based on a suitable…

The success of symplectic integrators for Hamiltonian ODEs has led to a decades-long program of research seeking analogously structure-preserving numerical methods for Hamiltonian PDEs. In this paper, we construct a large class of such…

We show that, when applied to any non-canonical Hamiltonian system, any integrator that is symplectic for canonical Hamiltonian problems is actually conjugate symplectic for the non-canonical structure. This result is useful because it…

Symplectic integrators are the tool of choice for many researchers studying dynamical systems because of their good long-term energy conservation properties. For systems with a dominant central mass, symplectic integrators are also highly…

A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the…