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

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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.