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The deep arbitrary polynomial chaos neural network or how Deep Artificial Neural Networks could benefit from data-driven homogeneous chaos theory.

, , , , , and . Neural Networks, (September 2023)

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Arbitrary multi-resolution multi-wavelet-based polynomial chaos expansion for data-driven uncertainty quantification., and . Reliab. Eng. Syst. Saf., (2022)Infering Boundary Conditions in Finite Volume Neural Networks., , , , , , and . ICANN (1), volume 13529 of Lecture Notes in Computer Science, page 538-549. Springer, (2022)Replication Data for: Learning Groundwater Contaminant Diffusion-Sorption Processes with a Finite Volume Neural Network., , , , , and . (November 2022)Composing Partial Differential Equations with Physics-Aware Neural Networks., , , , , and . ICML, volume 162 of Proceedings of Machine Learning Research, page 10773-10801. PMLR, (2022)Finite Volume Neural Network: Modeling Subsurface Contaminant Transport., , , , , and . CoRR, (2021)A fully Bayesian sparse polynomial chaos expansion approach with joint priors on the coefficients and global selection of terms., , , and . J. Comput. Phys., (September 2023)Reliability analysis with stratified importance sampling based on adaptive Kriging., , and . Reliab. Eng. Syst. Saf., (2020)Incomplete statistical information limits the utility of high-order polynomial chaos expansions., and . Reliab. Eng. Syst. Saf., (2018)The Connection between Bayesian Inference and Information Theory for Model Selection, Information Gain and Experimental Design., and . Entropy, 21 (11): 1081 (2019)Bayesian3 Active Learning for the Gaussian Process Emulator Using Information Theory., , , and . Entropy, 22 (8): 890 (2020)