Kinetic and related models with applications in the natural sciences

Model-Form Uncertainty Quantification for Probabilistic Graphical Models

Markos Katsoulakis

University of Massachusetts-Amherst

We discuss new information-based Uncertainty Quantification (UQ) methods cable to assess and improve the predictive ability of computational models in applications ranging from materials design, optimizing catalysts and fuel cells to risk assessment in subsurface flows. These models are typically multi-scale and involve any available data, e.g. from electronic structure calculations or observational/experiment data. Here we are formulating the problems as Probabilistic Graphical Models (PGM), whose hierarchical structure allows us to bring together in a systematic way statistical and multi scale physical modeling, as well as any data, which here are typically sparse. The resulting model-form uncertainty suggests there is not a single parametric representation for the model but rather a family of candidate non-parametric probabilistic representations. Furthermore, these models will necessarily have numerous sources of uncertainty/error arising in different components of the PGM. Such problems pose conceptual and computational challenges that are not easily addressed by traditional uncertainty quantification techniques. Here we discuss new information theoretic divergences, based on the Donsker--Varadhan variational principle , that yield tight, scalable & computable bounds/guarantees on model predictions for quantities of interest, across families of PGMs. We illustrate these tools in three data-infomed problems : a) quantifying the impact of multiple sources of uncertainty in mesoscale bayesian reaction networks that include electronic structure data, b) the design of efficient fuel cells under model uncertainty, and c) tackling uncertainty in subsurface flows, related to sparse available data. Finally, we propose a model-form Sensitivity Index, which allows us to rank the impact of each component of the PGM, and provide a systematic methodology to go back and update model components that underperform.