Online Nonstationary Heteroscedastic Gaussian Process for Active Learning of Physical Fields

Invited talk by Victor Cohen from the Swiss Data Science Center (SDSC)

Abstract: Wind tunnel testing remains the gold-standard technique to validate the aerodynamic properties of any object, despite the significant progress in computational fluid dynamics. 

In wind tunnels, we typically sample the domain of interest using a robotic (or human) probe and reconstruct the continuous flow field using interpolation techniques. 

The operational costs of wind tunnels are enormous, and reducing the sampling time is paramount to the efficient use of the facilities. 

We propose an active learning strategy paired with a sparse nonstationary heteroscedastic Gaussian Process regression algorithm to reduce the measurement time while providing an accurate mean flow field reconstruction. 

Our regression method involves jointly learning the mean and noise fields, which relies on an iterative EM-like algorithm. One of our main results is proving the convergence of the proposed algorithm under mild assumptions. 

Our sampling strategy combines an exploration phase, through a Metropolis-Hastings-inspired algorithm, and an exploitation phase, that relies on the estimated variance. The first phase ensures that we have enough samples to provide a good initial estimate and the second phase focuses on accurately estimating the heteroscedastic uncertainty. 

Numerical experiments on analytical fields show the efficiency of our approach, and real experiments performed in a large-scale wind tunnel facility validate it.

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