Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics
This work addresses sampling inefficiencies in computational physics and machine learning, though it appears incremental as it builds on existing Langevin dynamics frameworks.
The authors tackled the problem of inefficient sampling in Langevin dynamics by proposing a modified method that violates the detailed balance condition, resulting in accelerated relaxation to the target distribution and reduced correlation time in the steady state.
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs-Boltzmann one is performed under the detailed balance condition. In the present study, we propose a modified Langevin dynamics violating the detailed balance condition on the transition-probability formulation. We confirm that the numerical implementation of the proposed method actually demonstrates two major beneficial improvements: acceleration of the relaxation to the predetermined distribution and reduction of the correlation time between two different realizations in the steady state.