Mapping polynomial fitting into feedforward neural networks for modeling nonlinear dynamic systems and beyond |
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| Affiliation: | 1. School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019-1024, United States;2. Division of Applied Science, Weidlinger Associates Inc., New York, NY 10014-3656, United States;3. School of Engineering and Applied Science, Columbia University, New York, NY 10027-6699, United States;1. Institute for Economic Forecasting, Romanian Academy, Bucharest, Romania;2. School of Management and Institute of Finance, University of Leicester, Leicester, UK;1. Institute of Applied and Computational Mathematics, Foundation for Research and Technology - Hellas, Heraklion, Greece;2. Department of Civil Engineering and Engineering Mechanics, Columbia University, NY, USA;3. Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece;1. Department of Radiology, Tri-Service General Hospital, National Defense Medical Center, Taipei, Taiwan, ROC;2. Department of Surgery, Tri-Service General Hospital, National Defense Medical Center, Taipei, Taiwan, ROC;3. Department of Pathology, Tri-Service General Hospital, National Defense Medical Center, Taipei, Taiwan, ROC;4. Department of Healthcare Administration, Asia University, Taichung, Taiwan, ROC |
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| Abstract: | This study presents an explicit demonstration on constructing a multilayer feedforward neural network to approximate polynomials and conduct polynomial fitting. Built on an algebraic analysis of sigmoidal activation functions rather than incremental training, this work reveals the capability of the “universal approximator” by relating the “soft computing tool” to an important class of conventional computing tools widely used in modeling nonlinear dynamic systems and many other scientific computing applications. The authors strive to enable physical interpretations and afford full control when applying the highly adaptive, powerful yet subjective neural network approach. This work is a part of the effort of bridging the gap between the black-box and mechanics-based parametric modeling. |
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