Characterization of the errors of the FMM in particle simulations

The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of particle simulations in many application areas, such as electrostatics, particle formulations of fluid mechanics, and others. Although the literature on the subject provides theoretical error bounds for the FMM approximation, there are not many reports of the measured errors in a suite of computational experiments. We have performed such an experimental investigation, and summarized the results of about 1000 calculations using the FMM algorithm, to characterize the accuracy of the method in relation with the different parameters available to the user. In addition to the more standard diagnostic of the maximum error, we supply illustrations of the spatial distribution of the errors, which offers visual evidence of all the contributing factors to the overall approximation accuracy: multipole expansion, local expansion, hierarchical spatial decomposition (interaction lists, local domain, far domain). This presentation is a contribution to any researcher wishing to incorporate the FMM acceleration to their application code, as it aids in understanding where accuracy is gained or compromised.Comment: 34 pages, 38 image

Experimenting Abstraction Mechanisms Through an Agent-Based Hierarchical Planner

In this paper, an agent-based architecture devised to perform experiments on hierarchical planning is described. The planning activity results from the interaction of a community of agents, some of them being explicitly devoted to embed one or more existing planners. The proposed architecture allows to exploit the characteristics of any external planner, under the hypothesis that a suitable wrapper –in form of planning agent– is provided. An implementation of the architecture, able to embed one planner of the graphplan family, has been used to directly assess whether or not abstraction mechanisms can help to reduce the time complexity of the search on specific domains. Some preliminary experiments are reported, focusing on problems taken from the AIPS 2002, 2000 and 1998 planning competitions. Comparative results, obtained by assessing the performances of the selected planner (used first in a stand-alone configuration and then embedded into the proposed multi-agent architecture), put into evidence that abstraction may significantly speed up the search

Machine learning in hybrid hierarchical and partial-order planners for manufacturing domains

The application of AI planning techniques to manufacturing Systems is being widely deployed for all the tasks involved in the process, from product design to production planning and control. One of these problems is the automatic generation of control sequences for the entire manufacturing system in such a way that final plans can be directly use das the sequential control programs which drive the operation of manufacturing systems. Hybis is a hierarchical and nonlinear planner whose goal is to obtain partially ordered plans at such a level of detail that they can be use das sequential control programs for manufacturing systems. Currently, those sequential control programs are being generated by hand using modelling tools. This document describes a work whose aim is to improve the efficiency of solving problems with Hybis by using machine learning techniques. It implements a deductive learning method that is able to automatically acquire control knowledge (heuristics) by generating bounded explanations of the problem solving episodes. The learning approach builds on Hamlet, a system that learns control knowledge in the form of control rules.This work was partially supported by a grant from the Ministerio de Ciencia y Tecnología through projects TAP1999-0535-C02-02, TIC2001-4936-E, and TIC2002-04146-C05-05.Publicad