The Deep Arbitrary Polynomial Chaos Neural Network or How Deep Artificial Neural Networks Could Benefit From Data-Driven Homogeneous Chaos Theory

The Deep Arbitrary Polynomial Chaos Neural Network or How Deep Artificial Neural Networks Could Benefit From Data-Driven Homogeneous Chaos Theory

Sergey Oladyshkin, Timothy Praditia, Ilja Kroeker, Farid Mohammadi, Wolfgang Nowak, Sebastian Otte

Artificial Intelligence and Machine Learning are widely used in mathematical computing and physical modeling. Deep Artificial Neural Networks are popular but rely on Gaussian distribution of neural signals, which may not be true in various applications. To address this, we propose Deep arbitrary polynomial chaos neural networks, integrating homogeneous chaos theory into modern neural networks, allowing adaptive data-driven multi-variate orthonormal representations and capturing high-order neural effects. Benchmarking, including multiphase flow of carbon dioxide in porous media, shows that this novel concept outperforms conventional networks, promising better learning of complex phenomena. Further development is needed to address various porous media challenges.

Neural Networks 166, 85-104 (2023)
Corresponding Author: Sergey Oladyshkin

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