Numerical Methods for Modeling Atomistic Trajectories with Diffusion SDEs
Calderon, Christopher P.
Martinez, Josue G.
Carroll, Raymond J.
Sorensen, Danny C.
The stochastic dynamics of small scale systems are often not known fromﾠa prioriﾠphysical considerations. We present data-driven numerical methods which can be used to approximate the nonlinear stochastic dynamics associated with time series of system observables. Given a single time series coming from a simulation or experiment, our approach uses maximum likelihood type estimates to obtain a sequence of local stochastic differential equations. The local models coming from one times series are then patched together using a penalized spline procedure. We provide an effcient algorithm for achieving this which utilizes estimates of the local parameter covariance. We also use goodness-of-fit tests to quantitatively determine when an overdamped Langevin approxi- mation can be used to describe the data. For situations where the overdamped approximation fails, we show that other diffusive models can still be used to approximate the dynamics. In addition, we also briefly discuss how variation observed in different curves, calibrated from different time series, can provide information about "hidden" conformational degrees of freedom not explicitly included in the model and how clustering these curves can help one in learning about the effective underlying free energy surface governing the dynamics of the atomistic system. The methods presented are applied to simulations modeling forced time-dependent transport of potassium transport through a gramicidinﾠAﾠchannel, but have applicability to other forced (and unforced) systems.
Citable link to this pagehttps://hdl.handle.net/1911/102096
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