Model-form uncertainty remains a concern in all areas of mathematical modeling. Computational models are increasingly used to make predictions affecting high-consequence engineering design and policy decisions. Incomplete information about the phenomenon being represented and limitations in computational resources require approximations and simplifications that can lead to uncertainties in the model’s form and errors in predicted quantities of interest. Techniques to address these uncertainties are essential for understanding the reliability of such predictions. Furthermore, they have the potential to increase the range of applicability and enhance the predictive power of uncertain models. Development of these approaches is an active area of research and is often necessarily application-specific. This minisymposium brings together researchers from a variety of disciplines to discuss different methods of addressing model-form uncertainty, including Bayesian and non-Bayesian approaches.
*Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
10:30
- CANCELED - Calibration, Propagation, and Validation of Model Discrepancy Across Experimental Settings
Kathryn Maupin | Sandia National Laboratories | United States
Show details
Authors:
Kathryn Maupin | Sandia National Laboratories | United States
Laura Swiler | Sandia National Laboratories | United States
The Bayesian paradigm naturally integrates uncertainties from both experimental data and model formulation, including initial or boundary conditions, model form and parameters, and numerical approximation. However, model inadequacy due to model form error is unavoidable in many situations due to incomplete understanding of the underlying physics, in addition to uncertainties in calibration and validation data. Thus, infinite amounts of data may still result in inadequate models.
Calibrating a discrepancy model requires careful consideration regarding problem-specific formulation, parameter estimation, and uncertainty quantification. Furthermore, the validity of the combined model for the prediction of quantities of interest remains in question. A generalized approach to calibrating a model discrepancy function when a given computational model is expected to perform for multiple experimental configurations is presented. The proposed formulation targets systematic differences between observations and model predictions. The construction and propagation of the corrected model into a predictive setting is demonstrated in the context of Bayesian model calibration.
*Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
11:00
Embedded model error quantification and propagation in physical models
Khachik Sargsyan | Sandia National Laboratories | United States
Show details
Authors:
Khachik Sargsyan | Sandia National Laboratories | United States
Tiernan Casey | Sandia National Laboratories | United States
Habib Najm | Sandia National Laboratories | United States
The calibration of computational models of physical systems typically assumes that the computational model replicates the exact mechanism behind data generation. As a result, calibrated model parameters are often biased, leading to deficient predictive skills. This work will present a Bayesian inference framework for representing, quantifying, and propagating uncertainties due to model structural errors by embedding stochastic correction terms in the model. The embedded correction approach ensures physical constraints are satisfied, and renders calibrated model predictions meaningful and robust with respect to structural errors over multiple, even unobservable, quantities of interest. The physical inputs and correction parameters are simultaneously inferred via surrogate-enabled Markov chain Monte Carlo. With a polynomial chaos characterization of the correction term, the approach allows efficient decomposition of uncertainty that includes contributions from data noise, parameter posterior uncertainty, and model error. The developed structural error quantification workflow is implemented in UQ Toolkit (www.sandia.gov/uqtoolkit). We demonstrate the key strengths of this method on both synthetic examples and practical engineering applications.
11:30
- CANCELED - Characterizing model-form uncertainty in an inadequate model of anomalous transport
Teresa Portone | The University of Texas at Austin | United States
Show details
Authors:
Teresa Portone | The University of Texas at Austin | United States
Robert Moser | The University of Texas at Austin | United States
The advection-diffusion equation (ADE) is known to be an inadequate predictor of mean contaminant transport through heterogeneous porous media at the field scale. This inadequacy is caused by the mean state’s dependence on transport at a range of scales, the smallest of which can neither be observed nor resolved for practical problems. In this work, a model-form uncertainty representation is developed to account for this missing dependence. It is modeled as a stochastic linear operator appearing in the ADE, and model-form uncertainty is encapsulated in the stochasticity of its eigenvalues. Forward propagation of uncertainty in the porous medium through a high-fidelity model resolving all scales is used to observe the eigenvalues’ statistics directly. The observations are used to model the distributions of the eigenvalues as a function of the statistics of the medium, enabling extrapolation of the uncertainty representation to unobserved scenarios.
12:00
Representing model error in reduced models of interacting systems
Rebecca Morrison | University of Colorado, Boulder | United States
Show details
Author:
Rebecca Morrison | University of Colorado, Boulder | United States
In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain critical populations are truly consequential). Thus it is common to use greatly reduced models, in which only the interactions among the species of interest are retained. In this talk, I explore the use of an embedded and calibrated discrepancy operator to represent model error. The operator is embedded within the differential equations of the model, which allows the action of the operator to be interpretable. Moreover, it is constrained by available physical information, and calibrated over many scenarios. These qualities of the discrepancy model—interpretability, robustness to different scenarios, and physical-consistency---are intended to support reliable predictions under extrapolative conditions.