Justin A. Krometis

Jeff Borggaard, Nathan E. Glatt-Holtz, Justin A. Krometis

We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant). We present two particle methods that leverage the structure of the inverse problem to enable efficient computation of the forward map, one for time evolution problems and one for a Dirichlet boundary-value problem. The methods scale in a natural fashion to modern computational architectures, enabling substantial speedup for applications involving sparse observations and high-dimensional unknowns. Numerical examples of applications to Bayesian inference and numerical optimization are provided.

Anna R. Flowers, Christopher T. Franck, Robert B. Gramacy et al.

Collecting operationally realistic data to inform machine learning models can be costly. Before collecting new data, it is helpful to understand where a model is deficient. For example, object detectors trained on images of rare objects may not be good at identification in poorly represented conditions. We offer a way of informing subsequent data acquisition to maximize model performance by leveraging the toolkit of computer experiments and metadata describing the circumstances under which the training data was collected (e.g., season, time of day, location). We do this by evaluating the learner as the training data is varied according to its metadata. A Gaussian process (GP) surrogate fit to that response surface can inform new data acquisitions. This meta-learning approach offers improvements to learner performance as compared to data with randomly selected metadata, which we illustrate on both classic learning examples, and on a motivating application involving the collection of aerial images in search of airplanes.