Multilevel Monte Carlo Sampling on Heterogeneous Computer Architectures

Adcock, Christiane; Ye, Yinyu; Jofre, L.; Iaccarino, Gianluca

doi:10.1615/int.j.uncertaintyquantification.2020033179

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…The multilevel (ML) method [15,16], inspired by the multigrid solver idea in linear algebra, is based on evaluating realizations of Q from a hierarchy of models with different levels ℓ, ℓ = 0, . .…”

Section: Multilevel Monte Carlomentioning

confidence: 99%

Multifidelity Approaches for Uncertainty Estimation in Wildfire Spread Simulators

Valero¹,

Jofre²,

Torres³

2021

14th WCCM-ECCOMAS Congress

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A variety of wildfire models are currently used for prescribed fire management, fire behaviour studies and decision support during wildfire emergencies, among other applications. All these applications are based on predictive analysis, and therefore require careful estimation of aleatoric and epistemic uncertainties such as weather conditions, vegetation properties and model parameters. However, the large computational cost of high-fidelity computaional fluid dynamics models prohibits the straightforward utilization of traditional Monte Carlo methods. Conversely, low-fidelity fire models are several orders of magnitude faster but they typically do not provide enough accuracy and they do not resolve all relevant phenomena. Multifidelity frameworks offer a viable solution to this limitation through the efficient combination of high-and low-fidelity simulations. While high-fidelity models provide the required level of accuracy, low-fidelity simulations are used to economically improve the confidence on estimated uncertainty. In this work, we assessed the suitability of multifidelity methodologies to quantify uncertainty in wildfire simulations. A collection of different multifidelity strategies, including Multilevel and Control Variates Monte Carlo, were tested and their computational efficiency compared. Fire spread was predicted in a canonical scenario using popular simulators such as the Wildland-Urban Interface Fire Dynamics Simulator (WFDS) and FARSITE. Results show that multifidelity estimators allow speedups in the order of 100× to 1000× with respect to traditional Monte Carlo.

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Section: Multilevel Monte Carlomentioning

confidence: 99%

Multifidelity Approaches for Uncertainty Estimation in Wildfire Spread Simulators

Valero¹,

Jofre²,

Torres³

2021

14th WCCM-ECCOMAS Congress

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show abstract

“…It is important to note that, over the past years, multifidelity (MF) strategies to reduce the cost of the outer-loop problem by combining the accuracy of high-fidelity (HF) models, e.g., DNS and LES, with the speedup achieved by low-fidelity (LF) representations, e.g., RANS, DES and analytical functions/correlations, have been extensively developed [20][21][22][23][24] and applied to propagate uncertainty in large-scale multiphysics turbulent flows [25][26][27][28] and optimization problems [29][30][31][32]. As demonstrated in [12], the SGD approach of this study may be extended to incorporate MF aerodynamic models, a direction we leave for a future study.…”

Section: B Sources Of Uncertaintymentioning

confidence: 99%

Rapid Aerodynamic Shape Optimization Under Parametric and Turbulence Model Uncertainty: A Stochastic Gradient Approach

Jofre,

Doostan

2021

Preprint

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Aerodynamic optimization is ubiquitous in the design of most engineering systems interacting with fluids. A common approach is to optimize a performance function -subject to some constraints -defined by a choice of an aerodynamic model, e.g., turbulence RANS model, and at nominal operating conditions. Practical experience indicates that such a deterministic, i.e., single-point, approach may result in considerably sub-optimal designs when the adopted aerodynamic model does not lead to accurate flow predictions or when the actual operating conditions differ from those considered in the design. One approach to address this shortcoming is to consider an average or robust design, wherein the statistical moments of the performance function, given the uncertainty in the operating conditions and the aerodynamic model, is optimized. However, when the number of uncertain inputs is large or the performance function exhibits significant variability, an accurate evaluation of these moments may require a large number of forward and/or adjoint solves, at each iteration of a gradient-based scheme. This, in turn, renders the design of complex aerodynamic systems computationally expensive, if not infeasible. To tackle this difficulty, we consider a variant of the stochastic gradient descent method where, in each optimization iteration, a stochastic approximation of the objective, constraints, and their gradients are generated. This is done via a small number of forward/adjoint solves corresponding to random selections of the uncertain parameters and aerodynamic model. The methodology is applied to the robust optimization of the standard NACA-0012 airfoil in a low-Mach-number turbulent flow regime and subject to parametric and turbulence model uncertainty. With a cost that is a small factor larger than that of the deterministic approach, the stochastic gradient approach significantly improves the performance (mean and variance) of the aerodynamic design for a wide range of operating conditions and turbulence models.

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Multifidelity prediction in wildfire spread simulation: Modeling, uncertainty quantification and sensitivity analysis

Valero

Jofre

Torres

2021

Environmental Modelling & Software

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Multilevel Monte Carlo Sampling on Heterogeneous Computer Architectures

Cited by 3 publications

References 15 publications

Multifidelity Approaches for Uncertainty Estimation in Wildfire Spread Simulators

Multifidelity Approaches for Uncertainty Estimation in Wildfire Spread Simulators

Rapid Aerodynamic Shape Optimization Under Parametric and Turbulence Model Uncertainty: A Stochastic Gradient Approach

Multifidelity prediction in wildfire spread simulation: Modeling, uncertainty quantification and sensitivity analysis

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