Related papers: Hessian-free force-gradient integrators and their …
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…
A comprehensive linear stability analysis of force-gradient integrators and their Hessian-free variants is carried out by investigating the harmonic oscillator as a test equation. The analysis reveals that the linear stability of…
We present initial results of the use of Force Gradient integrators for lattice field theories. These promise to give significant performance improvements, especially for light fermions and large lattices. Our results show that this is…
We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow…
Quantum simulation has shown great potential in many fields due to its powerful computational capabilities. However, the limited fidelity can lead to a severe limitation on the number of gate operations, which requires us to find optimized…
We study a novel class of numerical integrators, the adapted nested force-gradient schemes, used within the molecular dynamics step of the Hybrid Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on the lattice, a…
Numerical lattice gauge theory computations to generate gauge field configurations including the effects of dynamical fermions are usually carried out using algorithms that require the molecular dynamics evolution of gauge fields using…
We discuss how dynamical fermion computations may be made yet cheaper by using symplectic integrators that conserve energy much more accurately without decreasing the integration step size. We first explain why symplectic integrators…
This paper proposes several explicit and implicit multistep frequency response optimized integrators considering first or second order derivative. A prediction-based method aiming at accelerating a novel power system transient simulation…
Projection-based integrators are effectively employed in high-precision systems with growing industrial success. By utilizing a projection operator, the resulting projection-based integrator keeps its input-output pair within a designated…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
Hessian-free (HF) optimization has been shown to effectively train deep autoencoders (Martens, 2010). In this paper, we aim to accelerate HF training of autoencoders by reducing the amount of data used in training. HF utilizes the conjugate…
Efficient fourth order symplectic integrators are proposed for numerical integration of separable Hamiltonian systems H(p,q)=T(p)+V(q). Symmetric splitting coefficients with five to nine stages are obtained by higher order decomposition of…
We developed a Hamiltonian inspired by ASQTAD and highly improved staggered quark (HISQ) actions and show how these Hamiltonians can be used for quantum simulations. Gate costs for the time evolution of these improved Hamiltonians are…
A grid-feeding converter system is added to a novel power system transient simulation scheme based on frequency response optimized integrators considering second order derivative. The converter system and its implementation in the…
Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they…
Frequency response optimized integrators considering second order derivative are proposed in this paper. Based on the proposed numerical integrators, and others which also consider second order derivative, this paper puts forward a novel…
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…
We present sixth- and eighth-order Hermite integrators for astrophysical $N$-body simulations, which use the derivatives of accelerations up to second order ({\it snap}) and third order ({\it crackle}). These schemes do not require previous…
This review gives an overview on the research of algorithms for dynamical fermions used in large scale lattice QCD simulations. First a short overview on the state-of-the-art of ensemble generation at the physical point is given. Followed…