Computation and Acceleration in Molecular Simulation

The virial equation of state (VEOS) is one equations in statistical thermodynamics establishing a connection between molecular and macro-scale descriptions. The major application of VEOS includes making predictions on the behavior and properties of chemical systems, which is especially useful when real chemical experiments to investigate chemical systems are hard to do or dangerous. The virial coefficients are important to know the characteristics and convergence of VEOS and thus critical to calculate accurately.
First, we propose mixed-precision approaches specializing in calculating the high-order virial coefficients of the Lennard-Jones (LJ) model on hybrid architectures including general CPUs and many-core coprocessors. With the rise of new many-core coprocessors such as graphics processing units (GPU) and Intel’s Many Integrated Core (MIC) architecture, a broad range of scientific applications have exploited tremendous parallelism which leads to dramatic acceleration. Floating point precision on these accelerators is a significant problem that needs to be carefully addressed. Obtaining accurate and precise results while achieving the best performance has been a major challenge in high performance computing, where high-precision floating point data types are unavailable or are much more expensive than low-precision floating point computations. To alleviate this drawback in calculating the virial coefficients of LJ model, mixed-precision approaches are proposed to overcome the potential precision limitation yielded in applying Wheatley’s algorithm (An algorithm proposed in 2013 by Richard Wheatley) to calculate the integrand of the coefficients, which leads to accurate results from 8th to 10th order virial coefficients while sustaining good performance on both Nvidia GPU and Intel Xeon Phi coprocessor. By combining the Mayer Sampling Monte Carlo (MSMC) method with the direct generation of configurations method using chain structure, we further calculate virial coefficients up to 16th order of LJ model.
Second, we propose an extension to Wheatley’s algorithm to calculate the high-order virial coefficients of the square well (SW) model. By applying the extension of Wheatley’s algorithm, integrating with the direct generation of configurations method including chain, tree and ring structure, accurate and precise results from 4th to 9th order for SW model are calculated. The methodology is general and is applicable to other discrete potentials.
Third, we apply machine learning techniques to evaluate virial coefficients of the hard sphere (HS) model. Machine learning techniques have been applied to many problems in the area of chemical simulations by circumventing the direct calculation, which is also very expensive in the evaluation of high-order virial coefficients. To resolve the problem, we first apply the distribution evaluation and multiple clustering algorithms including k-means, affinity propagation, mean shift, agglomerative clustering and so on to analyze the datasets containing all encoded configurations, numerator and denominator as necessary components in calculating the virial coefficients. Then we calculate the virial coefficient values from the 4th to 7th order by using a series of regression algorithms such as gradient boosting regression, support vector machine regression, Gaussian process, k-nearest neighbors, neural network, etc. Virial coefficients are obtained by evaluating the numerator and denominator separately. Although we are able to determine the various coefficients accurately, each order of the virial coefficients requires a different technique for best performance.