The amount of data in existence is growing exponentially. This has lead to the development of an unavoidable basin of attraction in data-driven uncertainty quantification (UQ) approaches for large-scale or high dimensional (UQ) problems. However, it is still in its infancy and new ideas are needed for this core research area.
The goal of our minisymposium is to provide a forum for this diverse group to discuss and share ideas for developing data-driven UQ approaches. These advanced UQ methods involve in (but not limited to) machine learning, neural network, model reduction as well as advances in Bayesian framework. Various applications will be used to show the performance of these improved UQ approaches.
14:00
Windowed Space-time Least-squares Petrov-Galerkin Projection for Nonlinear Model Reduction
Yukiko Shimizu | Sandia National Laboratories | United States
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Authors:
Yukiko Shimizu | Sandia National Laboratories | United States
Kevin Carlberg | Sandia National Lab | United States
Many methods used in UQ can be computationally expensive and can exhibit poor convergence rates. In comparison, reduced-order modeling (ROM) has shown to significantly reduce the computational cost of approximating the forward-order uncertainty model (FOM). To further overcome the computational costs in UQ, we can use the space-time least-squares Petrov-Galerkin projection method (ST-LSPG), which projects the FOM to a linear space-time subspace. ST-LSPG performs aggressive reduction of the time domain and provides a priori error bounds in terms of the best space-time approximation error. However, ST-LSPG incurs large computational cost by modifying the lower block triangular structure of the original model reduction problem. Hence, ST-LSPG requires a dense space-time solver whose complexity is linear in the number of time steps and cubic in the time dimension making it impractical for larger applications. To address this, we present the windowed ST-LSPG method (WST-LSPG), which divides the time domain into windows and calculates each window’s corresponding low-dimensional space-time trial subspace. As a result, the solver is fully space-time coupled within a window, but is sequential across the windows. Thus, the complexity is linear in the number of time windows, and cubic in the time dimension within the windows. In the presentation, we demonstrate that WST-LSPG exhibits improved behaviors than ST-LSPG, which can lead to further cost reduction in UQ modeling.
14:30
- CANCELED - Data-driven Approach for Uncertainty Quantification in Complex Systems with Arbitrary Density
Huan Lei | Michigan State University | United States
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Authors:
Huan Lei | Michigan State University | United States
Jing Li | Pacific Northwest National Laboratory | United States
Peiyuan Gao | Pacific Northwest National Laboratory | United States
Stinis Panos | Pacific Northwest National Laboratory | United States
Nathan A. Baker | Pacific Northwest National Laboratory | United States
One of the grand challenges in uncertainty quantification roots in the implicit knowledge of underlying distribution function of the complex system. Traditional approaches show limitations to quantify the uncertainty propagation associated with such systems. We develop a data-driven approach to accurately construct the surrogate model for the quantify of interest, which is irrespective of the dependency and the analytical form of the underlying distribution. Our method is demonstrated in challenging problem such high-dimensional PDE systems and chemical properties of realistic biomolecule system with respect to high dimensional conformational fluctuations.
15:00
- CANCELED - Uncertainty Quantification for Kinematic Wave Models Based on CDF Methods
Xinghui Zhong | Zhejiang University | China
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Author:
Xinghui Zhong | Zhejiang University | China
Cumulative density function (CDF) methods have gained popularity in the area of uncertainty quantification (UQ) in recent years. In this talk, we discuss the UQ framework for the probability distribution of the system state described by a kinematic wave model, based on the CDF method. The approach relies on Monte Carlo Simulations (MCS) of the fine-grained CDF equation of system state, as derived by the CDF method. This fine-grained CDF equation is solved via the method of characteristics. Each method of characteristics solution is far more computationally efficient than direct solution of the kinematic wave model, and the MCS estimator of the CDF converges relatively quickly. We verify the accuracy and robustness of our procedure via comparison with direct MCS of a particular kinematic wave system, the Saint-Venant equation.
15:30
Bayesian UQ analysis of Computer Models with Local Features Under the Presence of Non-nested Multi-fidelity Designs: Application to the WRF Model
Georgios Karagiannis | Durham University | United Kingdom
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Authors:
Georgios Karagiannis | Durham University | United Kingdom
Guang Lin | Purdue University | United States
Bledar Alexandros Konomi | University of Cincinnati | United States
Co-kriging allows uncertainty quantification (UQ) analysis of expensive computer models running at different fidelity levels. Motivated by the Weather Research and Forecasting (WRF) climate model with different resolutions, we present a new Bayesian treed co-kriging procedure. The new procedure extends the scope of co-kriging in two ways: it can be implemented when non-nested experimental designs are available, and it takes into account non-stationarity in the output of the computer model. To facilitate the computations, we design an efficient RJMCMC sampler, tailored to the proposed model, which involves collapsed blocks and direct simulation from conditional distributions. Our method allows the evaluation of a recursive Gaussian process emulator for the computer model output at each fidelity level under the presence of non-stationarity and non-nested designs. The good performance of our method is demonstrated on benchmark examples, and compared against existing methods. The proposed method is implemented for the UQ analysis of a large-scale climate modeling application that involves the WRF climate model.