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

9624687 Maldonado提议的研究的总体目标是启动一个研究项目，以促进、扩展和改进广义过钡理论技术的最新进展。该项目的长期目标是开发更普遍和多学科的应用，而近期目标将是开发一种适用于n阶摄动理论方法的自适应和计算经济的误差减少技术。本文提出的初步结果强烈表明，相对初级的两隐层人工神经网络（ANN）可以适当地训练用于此类应用。事实上，PI先前开发的GPT方法为人工神经网络的系统训练和自适应实现提供了一个独特的框架，该人工神经网络旨在预测并纠正与n阶GPT解决方案相关的错误。此外，确定这些计算的所有部分，可以利用大规模并行或可扩展的计算机也将被解决。PI教育计划的主要目标围绕着培养四个主要的持续职业活动，他认为这是他教育计划未来成功的关键因素。此外，这些活动是由PI根据几个月的实际评估和观察独家选择的，并且完全符合他的个性，背景和已知的才能。PI喜欢这些活动，除了作为一个人和一个教育者的自我实现之外，他们不寻求个人利益。这些活动没有特别的优先顺序或隐含的重要性，它们是：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。

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.