Gerald Baumgartner

Xiongming Dai, Gerald Baumgartner

We propose a generalized minimum discrepancy, which derives from Legendre's ODE and spherical harmonic theoretics to provide a new criterion of equidistributed pointsets on the sphere. A continuous and derivative kernel in terms of elementary functions is established to simplify the computation of the generalized minimum discrepancy. We consider the deterministic point generated from Pycke's statistics to integrate a Franke function for the sphere and investigate the discrepancies of points systems embedding with different kernels. Quantitive experiments are conducted and the results are analyzed. Our deduced model can explore latent point systems, that have the minimum discrepancy without the involvement of pseudodifferential operators and Beltrami operators, by the use of derivatives. Compared to the random point generated from the Monte Carlo method, only a few points generated by our method are required to approximate the target in arbitrary dimensions.

Xiongming Dai, Gerald Baumgartner

A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated the effective particles are, and the quicker and more accurate it is to approximate the hidden Markov model, especially for the nonlinear case. We propose a repetitive deterministic domain with median ergodicity for resampling and have achieved the lowest variances compared to the other resampling methods. As the size of the deterministic domain $M\ll N$ (the size of population), given a feasible size of particles, our algorithm is faster than the state of the art, which is verified by theoretical deduction and experiments of a hidden Markov model in both the linear and non-linear cases.

Xiongming Dai, Gerald Baumgartner

Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses randomly taking small steps within uncertain regions in the parameter space. We are the first to consider the posterior distribution of the objective as a mapping of samples in an infinite-dimensional Euclidean space where deterministic submanifolds are embedded and propose a new criterion by maximizing the weighted Riesz polarization quantity, to discretize rectifiable submanifolds via pairwise interaction. We study the characteristics of Chebyshev particles and embed them into sequential MCMC, a novel sampler with a high acceptance ratio that proposes only a few evaluations. We have achieved high performance from the experiments for parameter inference in a linear Gaussian state-space model with synthetic data and a non-linear stochastic volatility model with real-world data.

Tanzila Tabassum, Omer Subasi, Ajay Panyala et al.

In this work, we develop machine learning (ML) based strategies to predict resources (costs) required for massively parallel chemistry computations, such as coupled-cluster methods, to guide application users before they commit to running expensive experiments on a supercomputer. By predicting application execution time, we determine the optimal runtime parameter values such as number of nodes and tile sizes. Two key questions of interest to users are addressed. The first is the shortest-time question, where the user is interested in knowing the parameter configurations (number of nodes and tile sizes) to achieve the shortest execution time for a given problem size and a target supercomputer. The second is the cheapest-run question in which the user is interested in minimizing resource usage, i.e., finding the number of nodes and tile size that minimizes the number of node-hours for a given problem size. We evaluate a rich family of ML models and strategies, developed based on the collections of runtime parameter values for the CCSD (Coupled Cluster with Singles and Doubles) application executed on the Department of Energy (DOE) Frontier and Aurora supercomputers. Our experiments show that when predicting the total execution time of a CCSD iteration, a Gradient Boosting (GB) ML model achieves a Mean Absolute Percentage Error (MAPE) of 0.023 and 0.073 for Aurora and Frontier, respectively. In the case where it is expensive to run experiments just to collect data points, we show that active learning can achieve a MAPE of about 0.2 with just around 450 experiments collected from Aurora and Frontier.

Gerald Baumgartner, Konstantin Läufer, Vincent F. Russo

Design patterns are distilled from many real systems to catalog common programming practice. However, some object-oriented design patterns are distorted or overly complicated because of the lack of supporting programming language constructs or mechanisms. For this paper, we have analyzed several published design patterns looking for idiomatic ways of working around constraints of the implementation language. From this analysis, we lay a groundwork of general-purpose language constructs and mechanisms that, if provided by a statically typed, object-oriented language, would better support the implementation of design patterns and, transitively, benefit the construction of many real systems. In particular, our catalog of language constructs includes subtyping separate from inheritance, lexically scoped closure objects independent of classes, and multimethod dispatch. The proposed constructs and mechanisms are not radically new, but rather are adopted from a variety of languages and programming language research and combined in a new, orthogonal manner. We argue that by describing design patterns in terms of the proposed constructs and mechanisms, pattern descriptions become simpler and, therefore, accessible to a larger number of language communities. Constructs and mechanisms lacking in a particular language can be implemented using paradigmatic idioms.

Ryan D. L. Engle, Douglas D. Hodson, Michael R. Grimaila et al.

Quantum Key Distribution (QKD) is an innovative technology which exploits the laws of quantum mechanics to generate and distribute unconditionally secure cryptographic keys. While QKD offers the promise of unconditionally secure key distribution, real world systems are built from non-ideal components which necessitates the need to model and understand the impact these non-idealities have on system performance and security. OMNeT++ has been used as a basis to develop a simulation framework to support this endeavor. This framework, referred to as "qkdX" extends OMNeT++'s module and message abstractions to efficiently model optical components, optical pulses, operating protocols and processes. This paper presents the design of this framework including how OMNeT++'s abstractions have been utilized to model quantum optical components, optical pulses, fiber and free space channels. Furthermore, from our toolbox of created components, we present various notional and real QKD systems, which have been studied and analyzed.