CAREER: Adaptive Higher-Order Error Correction of NonlinearDiffusion Generalized Perturbation Theory Via a Neural Network

职业：通过神经网络对非线性扩散广义扰动理论进行自适应高阶误差校正

• 批准号: 9624687
• 负责人: Guillermo Maldonado
• 金额: $ 31万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2001-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9624687&HistoricalAwards=false
• 关键词: CAREER; Adaptive; Higher; Order; Error

9624687 Maldonado The general objective of the proposed research is to initiate a research program that would promote, extend, and improve recent advances in Generalized Pertarbatium Theory Techniques. The long-term goal of this project targets to exploit more general and multidisciplinary applications, while the near-term goal will target the development of an adaptive -and computationally economic- error reduction technique applicable to an nth order perturbation theory methodology. The preliminary results herein presented strongly suggest that a relatively rudimentary two-hidden-layer artificial neural network (ANN) can be suitably trained for this type of application. In fact, the GPT methodology previously developed by the PI provides a unique framework for the systematic training and adaptive implementation of an ANN designed to predict, and thus correct, the error associated with an nth order GPT solution. Moreover, identifying all portions of these calculations which can take advantage of massively parallel or scalable computers will also be addressed. The main objective of the PI's education plan revolves around nurturing four major ongoing career activities which he has identified as key contributing factors to the future success of his education plan. Furthermore, these activities have been selected exclusively by the PI based upon several moths of hands-on assessments and observations, and re in full agreement with his personality, background, and known talents. The PI enjoys these activities and seeks no personal gain from them other than selfulfillment as a person and as an educator. These activities, listed in no particular order of preference or implied importance, are: Active Learning Techniques. Encouraging Underrepresented Groups into Science and Engineering. Involving Undergraduate Students in Research. International Extensions of Research Efforts. The education plan of this proposal elaborates further on each of the above topics.

9624687 Maldonado 拟议研究的总体目标是启动一项研究计划，以促进、扩展和改进广义 Pertarbatium 理论技术的最新进展。 该项目的长期目标是开发更通用和多学科的应用，而近期目标是开发适用于 n 阶微扰理论方法的自适应且计算经济的误差减少技术。 本文提出的初步结果强烈表明，相对基本的两隐藏层人工神经网络（ANN）可以针对此类应用进行适当的训练。 事实上，PI 先前开发的 GPT 方法为 ANN 的系统训练和自适应实施提供了一个独特的框架，该框架旨在预测并从而纠正与 n 阶 GPT 解决方案相关的错误。 此外，还将解决识别这些计算中可以利用大规模并行或可扩展计算机的所有部分。 PI 教育计划的主要目标围绕培育四项主要的持续职业活动，他认为这些活动是其教育计划未来成功的关键因素。 此外，这些活动是由 PI 根据数个月的实践评估和观察专门选择的，并且与他的个性、背景和已知才能完全一致。 PI 喜欢这些活动，除了作为一个人和作为一名教育者的自我实现之外，不从这些活动中寻求任何个人利益。 这些活动（不按优先顺序或暗示重要性列出）是： 主动学习技巧。鼓励代表性不足的群体进入科学和工程领域。让本科生参与研究。研究工作的国际扩展。 本提案的教育计划进一步阐述了上述每个主题。