Data-driven supervised learning: Neural networks and uncertainty quantification

Bamdad Hosseini

In this talk I will discuss some ideas at the intersection of machine learning and uncertainty quantification with a particular focus on data-driven methods that do not require explicit knowledge of processes that generate the data. In the first half of the talk I will discuss supervised learning on Banach spaces for emulation of PDE based models and outline a method that combines principal component analysis with neural network regression for mesh-independent approximation of PDE solutions. In the second half I will take a different approach to supervised learning viewing it as a conditional sampling problem. I will then introduce a measure transport framework based on generative adversarial networks (GANs) for data-driven conditional sampling.
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