Despite the remarkable growth in computational power, it is still very computationally expensive to simulate most real-world systems in full detail, including a comprehensive analysis of parameter and model uncertainty. In such situations, data-driven approaches are tractable computational methods that provide useful empirical characterizations of uncertainty and have been successfully exploited in recent years. The increasing availability of very large data sets for this purpose makes techniques in machine learning an attractive toolbox for uncertainty emulation and characterization.
This minisymposium focuses on recent advances in uncertainty quantification algorithmic developments and applications based on data-driven and machine learning approaches in large-scale applications. Topics include data-driven surrogate construction, data assimilation, and physics-informed machine learning based on a limited number of data/observations and provide guidance for the system design, forecasting, etc.
08:30
- CANCELED - Model reduction of dynamical systems with deep convolutional autoencoders: hyper-reduction, ResNets, and application to UQ
Kevin Carlberg | Sandia National Laboratories Livermore | United States
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Authors:
Kookjin Lee | Sandia National Laboratories Livermore | United States
Kevin Carlberg | Sandia National Laboratories Livermore | United States
Model reduction provides a mechanism to make uncertainty-quantification with high-fidelity models computationally tractable. However, nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). To address this, we describe a novel framework for projecting dynamical systems onto nonlinear manifolds using minimum-residual formulations at the time-continuous and time-discrete levels; the former leads to manifold Galerkin projection, while the latter leads to manifold least-squares Petrov--Galerkin (LSPG) projection. In addition, we propose a computationally practical approach for computing the nonlinear manifold, which is based on convolutional autoencoders from deep learning. We also equip the resulting ROM with hyper-reduction to enable substantial computational-cost savings, and show how particular ResNet architectures can further reduce the ROM dimensionality.
09:00
- CANCELED - A bi-fidelity stochastic collocation method for multiscale kinetic equations with random parameters
Liu Liu | The University of Texas at Austin | United States
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Authors:
Liu Liu | The University of Texas at Austin | United States
Xueyu Zhu | University of Iowa | United States
In this talk, we will study kinetic equations with multiple scales and uncertainty by using a bi-fidelity stochastic collocation method. The bi-fidelity approximation can capture well the macroscopic quantities of the solution to the kinetic equation (high-fidelity solution) in the random space, with efficient computational and memory cost. We then develop a general framework to obtain an error estimate between the high-fidelity and bi-fidelity solutions in solving these problems. Extensive numerical experiments including evaluating a priori error estimate bound will be presented to verify the efficiency and accuracy of our proposed method.
09:30
- CANCELED - Optimal allocation of computational resources based on Gaussian Process
Yanyan He | University of North Texas | United States
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Authors:
Yanyan He | University of North Texas | United States
John Chilleri | New Mexico Tech | United States
Dmitry Bedrov | University of Utah | United States
Robert M. Kirby | University of Utah | United States
Multi-scale simulations have been intensively implemented in various disciplines to study the material properties or system behaviors on one level using information from different levels. However, extracting quantities from molecular dynamics (MD) simulations could be computational expensive, such as calculating the diffusivity especially at low temperatures. In this talk, we are going to discuss the optimal allocation of computational resources to MD simulations. Specifically, we propose a numerical optimization framework on time allocation to MD simulations based on Gaussian Processes (GPs), so that a surrogate model with uncertainty estimation can be constructed to approximate the true MD simulation. The proposed framework is demonstrated using a test case of a glass-forming system with divergent dynamic relaxations where a Gaussian Process is constructed to estimate the diffusivity and its uncertainty with respect to the temperature.
10:00
Sensor data integration using physics-informed, boundary-aware Gaussian processes
Mariella Kast | Ecole polytechnique fédérale de Lausanne | Switzerland
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Authors:
Mengwu Guo | Ecole polytechnique fédérale de Lausanne | Switzerland
Mariella Kast | Ecole polytechnique fédérale de Lausanne | Switzerland
Jan Hesthaven | Ecole polytechnique fédérale de Lausanne | Switzerland
A Bayesian framework is proposed to integrate sensor data into simulation models of
engineering Digital Twins. The prior of the calibrated solution field is expressed as a
linear combination of two Gaussian processes (GPs), one generated from the
simulation results and the other as a corrector. The simulation-based GP is defined
via a sampling over the domain of characterizing parameters, while the corrector GP
is set to be boundary-aware employing the eigen decomposition of the Laplacian
operator over the spatial domain, which ensures the satisfaction of Dirichlet
boundary conditions and a good performance of calibration. Conditioning on the
sensor data, the posterior GP gives an effective calibration of the solution field. The
proposed method avoids the inference of parameter values and directly corrects the
solution field with a physics-informed, boundary-aware nature, resulting in a
convenient and reliable scheme for the data integration of complex engineering
structures. In cooperation with a data-driven reduced basis model, good online
efficiency is achieved for the real-time updating of engineering Digital Twins.