DaPC NN: Deep Arbitrary Polynomial Chaos Neural Network

DaPC NN Matlab Toolbox: Deep Arbitrary Polynomial Chaos Neural Network
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Updated 29 Nov 2023

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Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial Neural Networks are very popular in our days. Depending on the learning task, the exact form of Deep Artificial Neural Networks is determined via their multi-layer architecture, activation functions and the so-called loss function. However, for a majority of deep learning approaches based on Deep Artificial Neural Networks, the kernel structure of neural signal processing remains the same, where the node response is encoded as a linear superposition of neurons, while the non-linearity is triggered by the activation functions. In the current Matlab Toolbox analyses the neural signal processing in Deep Artificial Neural Networks from the point of view of homogeneous chaos theory as known from polynomial chaos expansion introduced by Norbert Wiener in 1938. It employs the data-driven generalization of polynomial chaos expansion theory known as arbitrary polynomial chaos (aPC: Oladyshkin S. and Nowak W., 2012 and 2018) to construct a corresponding multi-layer representation of a Deep Artificial Neural Network. Doing so, we generalize the conventional structure of DANNs to Deep arbitrary polynomial chaos neural networks (DaPC NN: Oladyshkin et al. 2023).
AUTHOR:
Sergey Oladyshkin
AFFILIATION:
Stuttgart Research Centre for Simulation Technology,
Department of Stochastic Simulation and Safety Research for Hydrosystems,
Institute for Modelling Hydraulic and Environmental Systems,
University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart
CONTACT INFORMATION:
E-mail: Sergey.Oladyshkin@iws.uni-stuttgart.de
Phone: +49-711-685-60116
Fax: +49-711-685-51073
Website: http://www.iws.uni-stuttgart.de

Cite As

Sergey Oladyshkin (2024). DaPC NN: Deep Arbitrary Polynomial Chaos Neural Network (https://www.mathworks.com/matlabcentral/fileexchange/112110-dapc-nn-deep-arbitrary-polynomial-chaos-neural-network), MATLAB Central File Exchange. Retrieved .

Oladyshkin, S., and W. Nowak. “Data-Driven Uncertainty Quantification Using the Arbitrary Polynomial Chaos Expansion.” Reliability Engineering &Amp\Mathsemicolon System Safety, vol. 106, Elsevier BV, Oct. 2012, pp. 179–90, doi:10.1016/j.ress.2012.05.002.

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Oladyshkin, Sergey, and Wolfgang Nowak. “Incomplete Statistical Information Limits the Utility of High-Order Polynomial Chaos Expansions.” Reliability Engineering &Amp\Mathsemicolon System Safety, vol. 169, Elsevier BV, Jan. 2018, pp. 137–48, doi:10.1016/j.ress.2017.08.010.

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Oladyshkin S., Praditia T., Kroeker I., Mohammadi F., Nowak W., Otte S., The Deep Arbitrary Polynomial Chaos Neural Network or how Deep Artificial Neural Networks could benefit from Data-Driven Homogeneous Chaos Theory. Neural Networks. Elsevier, 2023. DOI: 10.1016/j.neunet.2023.06.036.

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Version Published Release Notes
0.0.4

Multivariate Polynomial Degrees

0.0.3

Alpha Version 0.0.3

0.0.2

Alpha Version 0.0.2

0.0.1