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.
14:00
A random matrix approach for quantifying model-form uncertainties in turbulence modeling
Heng Xiao | Virginia Tech | United States
Show details
Authors:
Heng Xiao | Virginia Tech | United States
Jianxun Wang | University of Notre Dame | United States
Roger Ghanem | University of Southern California | United States
With the ever-increasing use of Reynolds-Averaged Navier–Stokes (RANS) simulations in mission-critical applications, the quantification of model-form uncertainty in RANS models has attracted attention in the turbulence modeling community. In this work we propose a random matrix approach for quantifying model-form uncertainties in RANS simulations with the realizability of the Reynolds stress guaranteed, which is achieved by construction from the Cholesky factorization of the normalized Reynolds stress tensor. Furthermore, the maximum entropy principle is used to identify the probability distribution that satisfies the constraints from available information but without introducing artificial constraints. We demonstrate that the proposed approach is able to ensure the realizability of the Reynolds stress naturally. Numerical simulations on a typical flow with separation have shown physically reasonable results, which verify the proposed approach.
14:30
Improving generalization capabilities of physics-constrained data-augmented models
Vishal Srivastava | University of Michigan | United States
Show details
Authors:
Karthik Duraisamy | University of Michigan | United States
Vishal Srivastava | University of Michigan | United States
This talk focuses on the construction of data-augmented physics-based models that can learn from different systems, and transfer this modeling knowledge to make predictions in other systems that share similar physics. This defines a paradigm of transfer learning in the sense that the learning should target global rules - rather than problem-specific information - that is common to a class of systems that share similar physics. In the limit of finite (big or small) data, this requires the enforcement of physics-inspired and empirically-known constraints. We embed learning architectures within PDE models and train the hybrid model in an integrated fashion, strongly enforcing consistency between the learning and model construction. Examples of the enforcement of hard and soft constraints will be provided. These hybrid models are trained across different systems that are representative of the underlying model discrepancy, yielding predictions on unseen problems with quantified error bounds.
15:00
- CANCELED - Quantification and Calibration of Model-Form and Parameter Uncertainty in Stochastic Dynamics Models with Fractional Derivatives
Yan Wang | Georgia Institute of Technology | United States
Show details
Authors:
Yan Wang | Georgia Institute of Technology | United States
Baoqiang Zhang | Xiamen University | China
Classical dynamics and stochastic dynamics models rely on the assumption of integer-order differentiation in the mathematical formulation, which leads to model-form uncertainty in simulation predictions. In this research, fractional derivatives are introduced as the hyperparameters of models so that the discrepancy as a result of model-form errors can be minimized by calibrating the hyperparameters in the same way as regular system parameters. The model-form calibration process is demonstrated with fractional Fokker-Planck equations, where mutual information is used as the metric. The simultaneous Bayesian calibration of hyperparameters and parameters is further illustrated with a multi-degree vibration system where both types of parameters are optimized with the fractional frequency response function as the reference. Wang Y. (2016) Model form calibration in drift-diffusion simulation using fractional derivatives. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B, 2(3): 031006.
Zhang B., Guo Q., Wang Y., and Zhan M. (2019) Model-form and parameter uncertainty quantification in structural vibration simulation using fractional derivatives. Journal of Computational and Nonlinear Dynamics, 14(5): 051006.
15:30
A Bayesian Framework for Robust Decisions in the Presence of Misspecified Models
Chi Feng | Massachusetts Institute of Technology | United States
Show details
Authors:
Chi Feng | Massachusetts Institute of Technology | United States
Youssef Marzouk | Massachusetts Institute of Technology | United States
Measures of decision risk based on the distribution of losses over a posterior distribution obtained via standard Bayesian techniques may not be robust to model misspecification. With more observations, the posterior distribution concentrates onto a minimum Kullback-Leibler point, which leads to underestimated risk when using a misspecified model. We propose a generalized posterior distribution that instead concentrates onto multiple points in proportion to the fraction of observations that are consistent with the model. Our approach uses parameter-dependent data weights that result in a tapered likelihood function. We also introduce a parameter-dependent normalizer to the likelihood function so that the posterior probability is locally proportional to the fraction of data consistent with the model. The resulting generalized posterior is a ``doubly-intractable'' distribution in the sense that the normalizer (which now depends on the model parameters) cannot be eliminated in a Metropolis-Hastings acceptance probability. We use random series truncation and adaptive importance sampling to construct unbiased estimates of the generalized posterior density and compute posterior expectations using pseudo-marginal Markov-chain Monte Carlo. We demonstrate our approach on a healthcare application of target-controlled infusion using misspecified pharmacokinetic models.