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ADAPTIVE STEPSIZE ALGORITHMS FOR LANGEVIN DYNAMICS
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DOI：10.1137/24M1658590.png)
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We discuss the design of an invariant measure-preserving transformation for the numerical treatment of Langevin dynamics based on a rescaling of time, with the goal of sampling from an invariant measure. Given an appropriate monitor function which characterizes the numerical difficulty of the problem as a function of the state of the system, this method allows stepsizes to be reduced only when necessary, facilitating efficient recovery of long-time behavior. We study both overdamped and underdamped Langevin dynamics. We investigate how an appropriate correction term that ensures preservation of the invariant measure should be incorporated into a numerical splitting scheme. Finally, we demonstrate the use of the technique on several model systems, including a Bayesian sampling problem with a steep prior.
Keyword:
adaptivity
stochastic differential equation
timestep- ping
equilibrium sampling
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