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An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

The Separable Shadow Hybrid Monte Carlo (S2HMC) method for improved performence over Hybrid Monte Carlo.

Author: Christopher R. Sweet (University of Notre Dame)

Abstract

Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The Shadow Hybrid Monte Carlo (SHMC) was previously introduced to overcome this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. However SHMC's performance is limited by the need to generate momenta for the MD step from a non-separable shadow Hamiltonian. The Separable Shadow Hybrid Monte Carlo (S2HMC) method, based on a separable formulation of the shadow Hamiltonian, allows allows efficient generation of momenta and retains the advantage of SHMC.