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

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 (DANN) are very popular in our days. Depending on the learning task, the exact form of DANNs is determined via their multi-layer architecture, activation functions and the so-called loss function.

Bayesian Active Learning for the Gaussian Process Emulator Using Information Theory.

Gaussian process emulators (GPE) are a machine learning approach that replicates computational demanding models using training runs of that model. Constructing such a surrogate is very challenging and, in the context of Bayesian inference, the training runs should be well invested. The current paper offers a fully Bayesian view on GPEs for Bayesian inference accompanied by Bayesian active learning (BAL).

Probabilistic Assessment of Above Zone Pressure Predictions at a Geologic Carbon Storage Site.

Carbon dioxide (CO) storage into geological formations is regarded as an important mitigation strategy for anthropogenic CO emissions to the atmosphere. This study first simulates the leakage of CO and brine from a storage reservoir through the caprock. Then, we estimate the resulting pressure changes at the zone overlying the caprock also known as Above Zone Monitoring Interval (AZMI).