Surrogate modeling for stochastic simulators using statistical approaches
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2022-12-16
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Abstract
In the context of uncertainty quantification or optimization, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the output of which is a random variable for a given set of input parameters. To alleviate the computational burden, surrogate models are usually constructed and evaluated instead. However, due to the random nature of the model response, classical surrogate models cannot be applied directly to the emulation of stochastic simulators.
In this thesis, we propose two new approaches to emulate the entire response distribution of stochastic simulators: the generalized lambda model and the stochastic polynomial chaos expansion. The first one capitalizes on the use of the generalized lambda distribution to characterize the random response. The distribution parameters are functions of the input variables and are represented by polynomial chaos expansions. We explore replication-based methods to build generalized lambda models and improve their performance by an additional joint optimization. We further elaborate this idea and develop a new method that does not require replications. Using this surrogate, we investigate sensitivity analysis for stochastic simulators.
The second surrogate model, stochastic polynomial chaos expansions, overcomes the shortcomings of generalized lambda models, which are unable to represent multimodal distributions. In this more versatile stochastic emulator, we extend polynomial chaos expansions by introducing an artificial latent variable to the expansion and an additive noise variable to mimic the intrinsic stochasticity of the simulator. We also propose an adaptive algorithm to construct the surrogate model without the need for replications.
For both stochastic surrogate models, we develop some basic theoretical properties of the primary estimation method. Analytical examples and engineering applications, including wind turbine design and seismic fragility analysis, are used to validate and illustrate the performance of the new approaches. Furthermore, these engineering case studies provide valuable insights into the applicability of the developed framework to real-world industrial problems.
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ETH Zurich, Risk, Safety and Uncertainty Quantification
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Doctoral Examination - Public Part
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03962 - Sudret, Bruno / Sudret, Bruno
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175524 - Surrogate Modelling for Stochastic Simulators (SAMOS) (SNF)