Accelerating multiscale modelling of fluids with on-the-fly Gaussian process regression

Abstract

We present a scheme for accelerating hybrid continuum-atomistic models in multiscale fluidic systems by using Gaussian process regression as a surrogate model for computationally expensive molecular dynamics simulations. Using Gaussian process regression, we are able to accurately predict atomic-scale information purely by consideration of the macroscopic continuum-model inputs and outputs and judge on the fly whether the uncertainty of our prediction is at an acceptable level, else a new molecular simulation is performed to continually augment the database, which is never required to be complete. This provides a substantial improvement over the current generation of hybrid methods, which often require many similar atomistic simulations to be performed, discarding information after it is used once. We apply our hybrid scheme to nano-confined unsteady flow through a high-aspect-ratio converging–diverging channel, and make comparisons between the new scheme and full molecular dynamics simulations for a range of uncertainty thresholds and initial databases. For low thresholds, our hybrid solution is highly accurate—around that of thermal noise. As the uncertainty threshold is raised, the accuracy of our scheme decreases and the computational speed-up increases (relative to a full molecular simulation), enabling the compromise between accuracy and efficiency to be tuned. The speed-up of our hybrid solution ranges from an order of magnitude, with no initial database, to cases where an extensive initial database ensures no new MD simulations are required.

Multiscale simulation of enhanced water flow in nanotubes

“…In a multiscale fl ow simulation, the necessary coupling between the MD simulation and the continuum fl uid formulation can be of three forms-concurrent (i.e., the MD simulations run continually with the continuum simulation), 11 , 19 sequential (i.e., MD presimulations fi rst generate fl ow data as multidimensional libraries/interpolants, which are then used by subsequent continuum simulations), 8 , 22 or adaptive sequential/concurrent (i.e., using machine learning to switch optimally between the concurrent/sequential approaches). 23 We now present multiscale results from both concurrent and sequential simulations of pressure-driven water fl ows through NTs of different materials, but with fi xed pressure drops and similar diameters: 19 , 24 CNTs with D = 2.034 nm, boron nitride nanotubes (BNNTs) with D = 2.072 nm, and silicon carbide nanotubes (SiCNTs) with D = 2.062 nm (see and open symbols (for concurrent coupling results). 19 , 22 , 24 up to around L = 150 nm, beyond which MD is too computationally expensive to be practical.…”

Machine Learning Directed Optimization of Classical Molecular Modeling Force Fields

“…Some applications of GPR in molecular simulations include ML force fields 49−51 and property prediction. 52 In Bayesian optimization, which is a special case of surrogate-assisted optimization, the uncertainty estimates from GPR (or a similar model) are directly used to balance exploration and exploitation. Recent work demonstrates Bayesian optimization can efficiently calibrate force field parameters in coarse-grained models.…”

“…Gaussian process regression (GPR) is a popular nonparametric surrogate model that smoothly interpolates between training data. Some applications of GPR in molecular simulations include ML force fields − and property prediction . In Bayesian optimization, which is a special case of surrogate-assisted optimization, the uncertainty estimates from GPR (or a similar model) are directly used to balance exploration and exploitation.…”

Machine Learning Directed Optimization of Classical Molecular Modeling Force Fields

“…Gaussian process regression (GPR) is a popular nonparametric surrogate model that smoothly interpolates between training data. Applications of GPR in molecu-lar simulations include ML force fields [41][42][43] and property prediction [44]. In Bayesian optimization, which is a special case of surrogate-assisted optimization, the uncertainty estimates from GPR (or a similar model) are directly used to balance exploration and exploitation.…”