Information Geometry of Statistical Manifolds and Data Assimilation
Abstract
Mathematical models used to represent “reality” are invariably faulty due to a number of mutually reinforcing reasons. These include a lack of detailed knowledge of the relevant laws of nature, and spatiotemporal variability of model coefficients that is under-specified by data. More often than not, high-fidelity simulations are too expensive to adequately explore the parameter space, and one has to resort to low-fidelity (e.g., coarse-grained) models. Consequently, model predictions must be accompanied by a quantifiable measure of predictive uncertainty (e.g., error bars or confidence intervals) that accounts for such deficiencies. When available, observations should be used to reduce this uncertainty. Data assimilation presents its whole set of challenges, among which scarcity (in quality and/or quantity) of observations. The probabilistic framework provides a natural means to combine mathematical models and observations to obtain better models with explicit confidence guarantees. Scalable, robust and computationally efficient (data- and physics-aware) algorithms for making predictions over multiple spatiotemporal scales are of crucial importance to virtually every aspect of the AFOSR mission. Construction of such models poses multiple interconnected challenges: How to select the level of fidelity of the model such that it is both accurate and useful? How to construct improved scaled models that are consistent with fine-scale simulations (physics) and available observations (data)? How to condition each model, regardless of the reference scale, with all available information? Addressing such questions is further complicated by the curse of dimensionality, which acquires multiple meanings. For instance, enhancing the model fidelity often increases dimensionality of the parameter space; and the dimensionality of Bayesian data assimilation tends to become very high. An additional level of complexity is introduced when probability distributions that are used to describe a model’s inputs/outputs are themselves uncertain.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 21, 2022
- Source ID
- FA95502110381XX0
Entities
People
- Daniel M. Tartakovsky
Organizations
- Air Force Office of Scientific Research
- Stanford University
- United States Air Force