Computer simulation models a.k.a. simulators are used nowadays in virtually all fields of applied science and engineering. Usually, simulators that predict quantities of interests (QoI) as a function of input parameters are deterministic, i.e. they can be considered as a mapping from an input- to an output space. Running the simulator twice with the same input values provides identical outputs.
In contrast, so-called stochastic simulators contain hidden sources of uncertainty (e.g. latent variables) or uncontrollable inputs, on top of the well-identified and controllable inputs, meaning that repeated runs with the same inputs provides different results. Of interest is the resulting distribution of the QoI conditioned by the input (controllable) parameters. This distribution can be characterized in a rough way by replicating the runs of the simulator for the same controllable inputs. Unfortunately, in the context of uncertainty propagation and sensitivity analysis, handling stochastic simulators may be highly demanding due to these replications. One appropriate solution can be to use surrogate models (also referred to metamodels) to approximate the conditional expectation of the model, from a limited number of simulations.
In this MS, we will present recent developments in the field of surrogate models for stochastic simulators, be it for uncertainty propagation, sensitivity analysis or robust design.
08:30
Surrogate Model Development for Radiation Source Localization Using 3-D monte Carlo Transport Codes
Ralph Smith | North Carolina State University | United States
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Authors:
Ralph Smith | North Carolina State University | United States
Jared Cook | North Carolina State University | United States
Paul Miles | Sandia National Laboratories | United States
Frank Angers | University of Michigan | United States
Christopher Swenson | University of Michigan | United States
Brian Kiedrowski | University of Michigan | United States
In this presentation, we discuss the construction and verification of surrogate models for radiation source localization in a simulated urban environment. We employ the high-fidelity radiation transport code Monte Carlo N-Particle (MCNP) to simulate radiation sources, detectors, background, scattering, and cross-sections due to buildings. However, these simulations take on the order of minutes to hours and hence are not feasible for experimental design, Bayesian inference, or uncertainty propagation. To address this, we construct and verify differentiable surrogate models and illustrate their use for inferring the location and intensity of a radiation source in the simulated urban setting.
09:00
Sparse generalized lambda models for surrogating stochastic simulators
Xujia Zhu | ETH Zurich | Switzerland
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Authors:
Xujia Zhu | ETH Zurich | Switzerland
Bruno Sudret | ETH Zurich | Switzerland
Due to limited computational power, performing uncertainty quantification analyses with complex computational models can be a challenging task. This is even more severe in the context of stochastic simulators, the response of which is a random variable for a given input vector. To alleviate the burden, surrogate models are usually constructed to represent the original model. However, classical surrogate modeling methods cannot be directly applied to stochastic simulators, due to the random nature of the response. In this talk, we present a novel surrogate model—the generalized lambda model—to emulate the response PDF of stochastic simulators. This statistical model assumes that the response PDF belongs to the generalized lambda distribution family, and the associated distribution parameters as functions of the input are represented by polynomial chaos (PC) expansions. For a given set of PC basis functions, the construction of such a surrogate model does not require repeated model evaluations with the same input parameters. In the case of unknown basis set, a stepwise algorithm is developed to adaptively construct sparse PC approximations. The performance of the proposed method is illustrated on various analytical examples, in terms of both the response PDF approximation and sensitivity indices estimation accuracy. In addition, further applications to case studies in finance and agriculture are also discussed to show the applicability of the algorithm to real problems.
09:30
Chance constraint optimization of a complex system - Application to the design of a floating offshore wind turbine
Alexis Cousin | IFPEN and Ecole Polytechnique | France
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Authors:
Alexis Cousin | IFPEN and Ecole Polytechnique | France
Josselin Garnier | Ecole Polytechnique | France
Martin Guiton | IFPEN | France
Miguel Munoz Zuniga | IFPEN | France
Floating offshore wind turbines present many advantages but a major limitation is their cost. Our goal is to find a design that minimizes the cost of the anchoring system and that respects certain constraints ensuring the reliability of the structure. Specifically, the anchoring system must restrain the movement of the floating platform subjected to random wind and waves, avoid compression in the mooring lines, and withstand the cumulative damage caused by fatigue. All these constraints inherit the random characteristic of the marine conditions, of the material properties, and of the manufacturing uncertainties. We face an optimization problem with a deterministic cost function and three probabilistic constraints. Having to evaluate the failure probabilities at each loop of the optimization algorithm is the main difficulty. A naive approach such as the Monte Carlo method requires computing with a time consuming simulator many realizations of quantities such as the pitch, the tension and the fatigue. Since the computation cost of this approach is too high, we propose a methodology that takes into account the nature of the constraints to solve the problem in a reasonable time. First, we use a frequency approach for the fatigue constraint and the extreme value theory for the two other constraints. We then tackle the problem with the contribution of metamodels coupled with the Monte-Carlo method.
10:00
Tradeoffs between explorations and repetitions in variance-based sensitivity analysis for stochastic models
Gildas Mazo | INRA | France
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Author:
Gildas Mazo | INRA | France
Sensitivity analysis for stochastic models raises challenges both in theory and applications. The estimation of variance-based sensitivity indices can be based on Monte-Carlo sampling in which the model is repeated and the input space explored. Ideally, both the number of repetitions and the number of explorations should be large, but, since the computing budget is limited, a tradeoff has to be made. How this tradeoff affects the performance of the statistical estimators will be examined. Frameworks in which optimal tradeoffs can be defined and estimated will be presented. Some resulting methods for estimating the sensitivity indices will be studied theoretically and on simulations.