Uncertainty Quantification techniques are by now mature enough to address realistic, large scale problems of significant relevance. In this minisymposium, we focus in particular on complex fluid dynamics problems for engineering and environmental applications, that are fields in which computational science has traditionally played a major role. Several different kinds of UQ analyses naturally arise in these fields: forward UQ, optimization under uncertainty, inverse problem and data assimilation (e.g. for real-time control). In these scenarios, non-standard randomness might occur, and the complexity of the governing PDE equations further introduces significant and fascinating theoretical and computational challenges. In particular, polynomial-based UQ methods like Polynomial Chaos or Sparse grids collocation might not work well, in which case one has to resort to sampling methods, control variates, and more recently, machine learning techniques. Ad-hoc algorithms for high-performance computing are also relevant in this framework and welcome in this minisymposium.
14:00
Adaptive sampling for constructing complex aerodynamic response surfaces on the NASA High-Lift Common Research Model
Qiqi Wang | Massachusetts Institute of Technology | United States
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Authors:
John Moore | Flexcompute. Inc. | United States
Feilin Jia | Flexcompute. Inc. | United States
Qiqi Wang | Massachusetts Institute of Technology | United States
Zongfu Yu | University of Wisconsin Madison | United States
Adaptive sampling can significantly increase the accuracy of response surfaces and reduce the cost of its construction. Traditional high-fidelity CFD simulations, however, often takes hours if not days to complete. This latency makes adaptive sampling, which requires the simulations to run sequentially, very time-consuming. As a result, most industrial applications use static design of experiments, which allows the simulations to run concurrently, for constructing aerodynamic response surfaces. This study combines a fast CFD service, Flow360, with the state-of-the-art adaptive sampling technique. It demonstrates the feasibility of adaptive sampling when each simulation can be completed in minutes instead of days. The study also highlights the advantages of adaptive sampling for high-dimensional responses with complex features.
14:30
Importance sampling and approximate control variates for complex physical simulation
Trung Pham | University of Michigan | United States
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Authors:
Trung Pham | University of Michigan | United States
Alex Gorodetsky | University of Michigan | United States
John Jakeman | Sandia National Laboratories | United States
Gianluca Geraci | Sandia National Laboratories | United States
Multifidelity uncertainty quantification has become an indispensable tool for tacking both forward and inverse UQ for computationally expensive models. Both multilevel (for varying discretization levels) and multifidelity (for more general model ensembles) tools have been developed that use cheap-to-evaluate inaccurate (but correlated) models to accelerate the computation of statistics for high-fidelity computationally expensive models. In this context, sampling-based approaches that improve upon standard Monte Carlo algorithms have recently been proved effective in wide varying applications. Our recently developed approximate control variate technique can be used to analyze and improve many existing sampling approaches by explicitly breaking with the common recursive assumptions. In this talk we describe an extension of these approaches to the use of importance sampling, instead of Monte Carlo, with the aim of both sampling from un-normalized distributions arising from Bayesian inference as well as targeting the estimation of small probabilities (rare events). Computational examples are provided for a wide variety of systems, including PDEs arising in fluid dynamics.
15:00
Efficient Robust Design Optimization using Exploratory Data Analysis
Domenico Quagliarella | Centro Italiano Ricerche Aerospaziali (CIRA) | Italy
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Authors:
Domenico Quagliarella | Centro Italiano Ricerche Aerospaziali (CIRA) | Italy
Elisa Morales Tirado | Centro Italiano Ricerche Aerospaziali (CIRA) | Italy
Andrea Bornaccioni | Roma Tre University | Italy
Robust and reliability-based design optimization is gaining increasing favor in the industrial context, especially in those application fields where classical deterministic design approaches lead to optimal design solutions excessively sensitive to production tolerances and operating conditions stability. Unfortunately, there is no free lunch, and the robust design loop is often much more expensive if compared to classical ones. Exploratory data analysis and statistical hypothesis testing techniques can help reduce and control the computational load required by robust or reliability-based design optimization procedures. Indeed, rather than trying to estimate the quantity of interest to optimize with a given, high, accuracy, we are interested in testing the behavior of an optimization algorithm with increasing levels of noise in the objective function evaluation. Therefore, statistical hypothesis testing and exploratory data analysis techniques, that are powerful tools to assess the reliability of statistical predictions, are used to investigate how classical evolutionary algorithms, like GAs and CMA-ES, are resistant to noise and hence to what extent they are useful in robust design optimization problems with coarse estimation of the quantities of interest. The proposed approach is applied to an aerodynamic shape design problem.
15:30
- NEW - A multilevel stochastic gradient algorithm for PDE-constrained optimal control problems under uncertainty
Fabio Nobile | Ecole Polytechnique Fédérale de Lausanne (EPFL) | Switzerland
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Authors:
Fabio Nobile | Ecole Polytechnique Fédérale de Lausanne (EPFL) | Switzerland
Matthieu Martin | CRITEO | France
Panagiotis Tsilifis | General Electric | United States
Sebastian Krumscheid | RWTH Aachen University | Germany
We consider an optimal control problem for an elliptic PDE with random coefficients. The control function is a deterministic, distributed forcing term that minimizes an expected quadratic regularized loss functional. For its numerical treatment we propose and analyze a multilevel stochastic gradient (MLSG) algorithm which uses at each iteration a full, or randomized, multilevel Monte Carlo estimator of the expected gradient, build on a hierarchy of finite element approximations of the underlying PDE. The algorithm requires choosing proper rates at which the finite element discretization is refined and the Monte Carlo sample size increased over the iterations. We present complexity bounds for such algorithm. In particular, we show that if the refinement rates are properly chosen, in certain cases the asymptotic complexity of the full MLSG algorithm in computing the optimal control is the same as the complexity of computing the expected loss functional for one given control by a standard multilevel Monte Carlo estimator.