ITR: A New Computational Paradigm: Robustness as a Resource

在计算科学的许多领域中，数值稳健性和几何一致性问题是众所周知的。问题是，不精确的计算机算法会导致不正确和不一致的几何结论(例如，在三角形内或外是点)。虽然计算机变得越来越快，但软件并没有变得更健壮。事实上，目前的趋势是更加缺乏稳健性。我们提出了一种新的计算范式来扭转这一趋势。健壮性通常被视为一个要么全有要么全无的命题。我们的新范式在于将健壮性视为一种计算资源，并在速度等其他资源之间进行权衡。每个程序都定义了一条特定的健壮性-速度折衷曲线；我们希望能够在该曲线上的任何点运行该程序。这项提议将开发技术，使这一能力有效并易于所有程序员访问。因此，任何程序员都可以生成早期的普通C/C++代码，这些代码可以健壮地运行。这一范式的含义是广泛的，并将把稳健性研究的成果带到主流计算中。我们建议(1)进行基础研究以支持这一新的计算范式，(2)创造实现这一范式的技术和软件工具，(3)探索快速且通常稳健的算法在算法设计中的应用。对于(1)，我们将专注于效率问题，如新的根界，增量计算，保证初等函数的绝对精度。对于(2)，我们预计将显著扩展我们的Core库的能力、效率和可用性，并包括诸如符号扰动等功能。最后，(3)的一个例子涉及几何结构检查的一般问题及其在新的有效几何算法中的应用。我们建议将我们的健壮性技术和软件应用到两个众所周知的非健壮性问题的重要应用中：*网格生成：我们将构建第一个完全健壮的网格生成器，它将被部署在主要的LOW求解器系统Cart3d中。*几何建模：我们将构建一个健壮的几何建模器，这将是第一个对精度敏感的此类系统。这项建议涉及与德国Max-Planck计算机科学研究所的Mehlhorn教授的算法和复杂性小组的国际合作。我们的国内合作者是NASAAmes研究中心的Michael Aftosmis(研究网格生成)和AT&T研究实验室的Shankar Krishnan(研究几何建模)。

The problem of numerical robustness and geometric consistency is well knownin many areas of computational science. The issue is that inexact computer arith-metic leads to incorrect and inconsistent geometric conclusions (for example, is apoint inside or outside a triangle). While computers are getting faster, softwareis not getting more robust. Indeed, the trend is towards more nonrobustness. Wepropose a new computational paradigm to reverse this trend.Robustness is often seen as an all-or-nothing proposition. Our new paradigmconsists in viewing robustness as a computational resource, to be traded off againstother resources such as speed. Each program defines a certain robustness-speedtrade-off curve; we want to be able to run the program at any point along thiscurve. This proposal will develop the technology to make this capability effcientand easily accessible to all programmers. As a result, any programmer can producenearly ordinary C/C++ code which can be run robustly. The implications of thisparadigm are wide ranging, and will bring the fruits of robustness research intomainstream computing.We propose to (1) conduct basic research to support this new computingparadigm, (2) to create the technology and software tools to achieve this paradigm,and (3) to explore the applications of fast and usually robust algorithms in algo-rithm design. For (1), we will focus on effciency issues such as novel root bounds,incremental computation, guaranteed absolute precision for elementary functions.For (2), we expect to significantly extend the power, efficiency and usability of ourCore Library and include capabilities such as symbolic perturbation. Finally anexample of (3) concerns the general problem of checking of geometric structures andtheir applications in new efficient geometric algorithms.We propose to apply our robustness techniques and software to two significantapplications in which nonrobustness problems are well-known:* Mesh Generation: we will construct the first fully robust mesh generator whichwill be deployed in a major ow solver system, Cart3d.* Geometric Modeling: we will build a robust geometric modeler which will bethe first such system that is precision-sensitive.This proposal involves international collaboration with Professor Mehlhorn'sAlgorithms and Complexity Group at the Max-Planck Institute of Computer Sci-ence in Germany. Our domestic collaborator are Michael Aftosmis from NASAAmes Research Center (on mesh generation) and Shankar Krishnan from AT&TResearch Laboratories (on geometric modeling).