Thursday, December 14, 2023
1:00 PM CST
USACM UQ Virtual Seminar
Gaussian Processes for Multi-source Learning and Solving PDEs
Ramin Bostanabad, University of California, Irvine
Modeling complex systems such as materials with unprecedented properties is increasingly relying on exploring vast input spaces via computer models. In many applications, this exploration is challenged by two major uncertainty sources: (1) lack of data (especially high-fidelity samples), and (2) inherent biases of computer models that arise from, e.g., missing physics, numerical errors, or approximations. Quantifying the effects of these uncertainty sources is especially difficult when models are computationally expensive and their input space has qualitative variables.
In this talk, we argue that Gaussian processes (GPs) provide a promising avenue for collectively quantifying these uncertainties and devising strategies for reducing them. Specifically, we design parametric mean and covariance functions that provide GPs with a number of advantages such as (1) learning from an arbitrary number of (noisy) data sources while quantifying both epistemic and aleatoric uncertainties, and (2) solving complex PDEs without using any labeled data in the domain. We will demonstrate these features via multiple examples where, time permitting, we also introduce novel strategies for adaptive multi-source sampling and anomaly detection.