PREDICTING PARALLEL APPLICATION PERFORMANCE VIA MACHINE LEARNING APPROACHES

Consistently growing architectural complexity and machine scales make creating accurate performance models for large-scale applications increasingly challenging. Traditional analytic models are difficult and time-consuming to construct, and are often unable to capture full system and application complexity. To address these challenges, we automatically build models based on execution samples. We use multilayer neural networks, since they can represent arbitrary functions and handle noisy inputs robustly. In this thesis, we focus on two well known parallel applications whose variations in execution times are not well understood: SMG2000, a semicoarsening multigrid solver, and HPL, an open source implementation of LINPACK. We sparsely sample performance data on two radically different platforms across large, multi-dimensional parameter spaces and show that our models based on this data can predict performance within 2% to 7% of actual application runtimes.National Science Foundation Grant Number CCF-0444413; United States Department of Energy Grant Number W-7405-Eng-4

Enumeration of self-avoiding walks on the square lattice

We describe a new algorithm for the enumeration of self-avoiding walks on the square lattice. Using up to 128 processors on a HP Alpha server cluster we have enumerated the number of self-avoiding walks on the square lattice to length 71. Series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and mean-square distance of monomers from the end points have been derived to length 59. Analysis of the resulting series yields accurate estimates of the critical exponents $\gamma$ and $\nu$ confirming predictions of their exact values. Likewise we obtain accurate amplitude estimates yielding precise values for certain universal amplitude combinations. Finally we report on an analysis giving compelling evidence that the leading non-analytic correction-to-scaling exponent $\Delta_1=3/2$.Comment: 24 pages, 6 figure

Newton Method on Riemannian Manifolds: Covariant Alpha-Theory

In this paper we study quantitative aspects of Newton method for finding zeros of mappings f: M_n -> R^n and vector fields X: M_x -> TM_

Constructing Parsimonious Analytic Models for Dynamic Systems via Symbolic Regression

Developing mathematical models of dynamic systems is central to many disciplines of engineering and science. Models facilitate simulations, analysis of the system's behavior, decision making and design of automatic control algorithms. Even inherently model-free control techniques such as reinforcement learning (RL) have been shown to benefit from the use of models, typically learned online. Any model construction method must address the tradeoff between the accuracy of the model and its complexity, which is difficult to strike. In this paper, we propose to employ symbolic regression (SR) to construct parsimonious process models described by analytic equations. We have equipped our method with two different state-of-the-art SR algorithms which automatically search for equations that fit the measured data: Single Node Genetic Programming (SNGP) and Multi-Gene Genetic Programming (MGGP). In addition to the standard problem formulation in the state-space domain, we show how the method can also be applied to input-output models of the NARX (nonlinear autoregressive with exogenous input) type. We present the approach on three simulated examples with up to 14-dimensional state space: an inverted pendulum, a mobile robot, and a bipedal walking robot. A comparison with deep neural networks and local linear regression shows that SR in most cases outperforms these commonly used alternative methods. We demonstrate on a real pendulum system that the analytic model found enables a RL controller to successfully perform the swing-up task, based on a model constructed from only 100 data samples