Uncertainty Quantification (UQ) is a modern research area at the intersection of applied mathematics, probability, statistics, computational science and engineering.  UQ is an essential component of predictive science, allowing scientists and engineers to make meaningful inferences and decisions based on imperfect physical models.

The UQ group has broad interests from foundational theoretical questions (e.g. fundamental limits on uncertainty or predictive capability) to practical numerical computation (e.g. efficient and robust calculation of uncertainties).  Our research interests include:

  • optimal and robust uncertainty quantification under epistemic uncertainty;
  • consistency and robustness of Bayesian procedures, with particular emphasis on the well-posedness of Bayesian inverse problems for infinite-dimensional, non-parametric, or functional unknkowns, and on dimension-independent computational methods;
  • probabilistic numerical methods for ordinary and partial differential equations and for high-dimensional numerical linear algebra;
  • the analysis of modes (MAP estimators) for infinite-dimensional, non-parametric, or functional inverse problems;
  • kernel-based machine learning methods for inference, e.g. conditional mean embedding, with application to time series analysis;
  • concentration-of-measure phenomena;
  • applications to seismic safety, optical properties of novel metamaterials, and hypervelocity impact and other high strain-rate deformations;
  • ...