Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points.

We present a global sensitivity analysis that quantifies the impact of parameter uncertainty on model outcomes. Specifically, we propose variance‐decomposition‐based Sobol' indices to establish an importance ranking of parameters and univariate effects to determine the direction of their impact. We employ the state‐of‐the‐art approach of constructing a polynomial chaos expansion of the model, from which Sobol' indices and univariate effects are then obtained analytically, using only a limited number of model evaluations. We apply this analysis to several quantities of interest of a standard real‐business‐cycle model and compare it to traditional local sensitivity analysis approaches. The results show that local sensitivity analysis can be very misleading, whereas the proposed method accurately and efficiently ranks all parameters according to importance, identifying interactions and nonlinearities. Computational techniques uncertainty quantification sensitivity analysis polynomial chaos expansion C60 C63

Uncertainty quantification and sensitivity analysis are essential for improving the modeling and estimation of greenhouse gas emissions in livestock farming to evaluate and reduce the impact of uncertainty in input parameters to model output. The present study is a comprehensive review of the sources of uncertainty and techniques used in uncertainty analysis, quantification, and sensitivity analysis. The search process involved rigorous selection criteria and articles retrieved from the Science Direct, Google Scholar, and Scopus databases and exported to RAYYAN for further screening. This review found that identifying the sources of uncertainty, implementing quantifying uncertainty, and analyzing sensitivity are of utmost importance in accurately estimating greenhouse gas emissions. This study proposes the development of an EcoPrecision framework for enhanced precision livestock farming, and estimation of emissions, to address the uncertainties in greenhouse gas emissions and climate change mitigation.

Computational modeling of cardiac electrophysiology (EP) has recently transitioned from a scientific research tool to clinical applications. To ensure reliability of clinical or regulatory decisions made using cardiac EP models, it is vital to evaluate the uncertainty in model predictions. Model predictions are uncertain because there is typically substantial uncertainty in model input parameters, due to measurement error or natural variability. While there has been much recent uncertainty quantification (UQ) research for cardiac EP models, all previous work has been limited by either: (i) considering uncertainty in only a subset of the full set of parameters; and/or (ii) assigning arbitrary variation to parameters (e.g., ±10 or 50% around mean value) rather than basing the parameter uncertainty on experimental data. In our recent work we overcame the first limitation by performing UQ and sensitivity analysis using a novel canine action potential model, allowing all parameters to be uncertain, but with arbitrary variation. Here, we address the second limitation by extending our previous work to use data-driven estimates of parameter uncertainty. Overall, we estimated uncertainty due to population variability in all parameters in five currents active during repolarization: inward potassium rectifier, transient outward potassium, L-type calcium, rapidly and slowly activating delayed potassium rectifier; 25 parameters in total (all model parameters except fast sodium current parameters). A variety of methods was used to estimate the variability in these parameters. We then propagated the uncertainties through the model to determine their impact on predictions of action potential shape, action potential duration (APD) prolongation due to drug block, and spiral wave dynamics. Parameter uncertainty had a significant effect on model predictions, especially L-type calcium current parameters. Correlation between physiological parameters was determined to play a role in physiological realism of action potentials. Surprisingly, even model outputs that were relative differences, specifically drug-induced APD prolongation, were heavily impacted by the underlying uncertainty. This is the first data-driven end-to-end UQ analysis in cardiac EP accounting for uncertainty in the vast majority of parameters, including first in tissue, and demonstrates how future UQ could be used to ensure model-based decisions are robust to all underlying parameter uncertainties.

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

Uncertainty quantification in a resonant nonlinear MEMS structure

Here, we examine the suitability of truncated Polynomial Chaos Expansions (PCE) and truncated Gram-Charlier Expansions (GrChE) as possible methods for uncertainty quantification (UQ) in nonlinear systems with intermittency and positive Lyapunov exponents.These two methods rely on truncated Galerkin projections of either the system variables in a fixed polynomial basis spanning the 'uncertain' subspace (PCE) or a suitable eigenfunction expansion of the joint probability distribution associated with the uncertain evolution of the system (GrChE).Based on a simple, statistically exactly solvable non-linear and non-Gaussian test model, we show in detail that methods exploiting truncated spectral expansions, be it PCE or GrChE, have significant limitations for uncertainty quantification in systems with intermittent instabilities or parametric uncertainties in the damping.Intermittency and fat-tailed probability densities are hallmark features of the inertial and dissipation ranges of turbulence and we show that in such important dynamical regimes PCE performs, at best, similarly to the vastly simpler Gaussian moment closure technique utilized earlier by the authors in a different context for UQ within a framework of Empirical Information Theory.Moreover, we show that the non-realizability of the GrChE approximations is linked to the onset of intermittency in the dynamics and it is frequently accompanied by an erroneous blow-up of the second-order statistics at short times.These limitations of the two types of truncated spectral expansions arise from the following: (i) Non-uniform convergence in time of PCE and GrChE resulting in a rapidly increasing number of terms necessary for a good approximation of the random process as time evolves, (ii) Fundamental problems with capturing the constant flux of randomness due to white Gaussian noise forcing via finite truncations of the spectral representation of the associated Wiener process, (iii) Slow decay of PCE and GrChE coefficients in the presence of intermittency, hampering implementation of sparse truncation methods which have been widely used in nearly elliptic problems or in low Reynolds number flows.Rigorous justification of these limitations is richly illustrated by straightforward tests exploiting a simple nonlinear and non-Gaussian but statistically exactly solvable test model which is proposed here as a challenging benchmark for algorithms for UQ in systems with intermittency.

Uncertainty quantification and sensitivity analysis of thermoacoustic stability with non-intrusive polynomial chaos expansion

The purpose of history matching is to achieve geological realizations calibrated to the historical performance of the reservoir. For complex geological structures it is usually intractable to run tens of thousands of full reservoir simulation to trace the most probable geological model. Hence the inadequacy of the history-matching results frequently leads to poor estimation of the true model and high uncertainty in production forecasting. Reduced-order modeling procedures, which have been applied in many application areas including reservoir simulation, represent a promising means for constructing efficient surrogate models. Nonlinear dimensionality reduction techniques allow for encapsulating the high-resolution complex geological description of reservoir into a low-dimensional subspace, which significantly reduces number of unknowns and provides an efficient way to construct a proxy model based on the the reduced-dimension parameters. Polynomial Chaos Expansions (PCE) is a powerful tool to quantify uncertainty in dynamical system when there is probabilistic uncertainty in the system parameters. In reservoir simulation it has been shown to be more accurate and efficient compared to traditional experimental design (ED). PCEs have a significant advantage over other response surfaces as the convergence to the true probability distribution is proved when the order of the PCE is increased. Accordingly PCE proxy can be used as the pseudo-simulator to represent the surface responses of the uncertain variables. When the objective and constraints of a reservoir model is described by multivariate polynomial functions, there are very efficient algorithms to compute the global solutions. We have developed a workflow at which incorporates PCE to find the global minimum of the misfit surface and assess the uncertainty associated with. The accuracy of the PCE proxy increases with the additional trial runs of the reservoir simulator. We conduct a two dimensional synthetic case study of a fluvial channel as well as a real field example to demonstrate the effectiveness of this approach. Kernel Principal Component Analysis (KPCA) is used to parameterize the complex geological structure. The study has revealed useful reservoir information and delivered more reliable production forecasts. PCE-based history match enhances the quality and efficiency of the estimation of the most probable geological model and improve the confidence interval of production forecasts.

Development and uncertainty analysis of the dynamic simulation for HFETR with BMUS framework

Multi-scale stochastic dynamic response analysis of offshore risers with lognormal uncertainties

Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are essential for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study presents one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.

Polynomial chaos (PC) expansions are used for the propagation of uncertainty through dynamical systems as an alternative to Monte Carlo methods. Model parameters in a given dynamical system are assumed to have known expansions, which correspond to simple standard distributions, and one is usually interested in the polynomial expansion of the system solution. We are concerned with the problem of estimating the PC expansion of a parameter vector when only realizations from its distribution are given. To this end we apply ideas from optimal transportation theory and network optimization.

Recent efforts to ensure the reliability of computational model-based predictions in healthcare, such as the ASME V&V40 Standard, emphasize the importance of uncertainty quantification (UQ) and sensitivity analysis (SA) when evaluating computational models. UQ involves empirically determining the uncertainty in model inputs—typically resulting from natural variability or measurement error—and then calculating the resultant uncertainty in model outputs. SA involves calculating how uncertainty in model outputs can be apportioned to input uncertainty. Rigorous comprehensive UQ/SA provides confidence that model-based decisions are robust to underlying uncertainties. However, comprehensive UQ/SA is not currently feasible for whole heart models, due to numerous factors including model complexity and difficulty in measuring variability in the many parameters. Here, we present a significant step to developing a framework to overcome these limitations. We: (i) developed a novel action potential (AP) model of moderate complexity (six currents, seven variables, 36 parameters); (ii) prescribed input variability for all parameters (not empirically derived); (iii) used a single “hyper-parameter” to study increasing levels of parameter uncertainty; (iv) performed UQ and SA for a range of model-derived quantities with physiological relevance; and (v) present quantitative and qualitative ways to analyze different behaviors that occur under parameter uncertainty, including “model failure”. This is the first time uncertainty in every parameter (including conductances, steady-state parameters, and time constant parameters) of every ionic current in a cardiac model has been studied. This approach allowed us to demonstrate that, for this model, the simulated AP is fully robust to low levels of parameter uncertainty — to our knowledge the first time this has been shown of any cardiac model. A range of dynamics was observed at larger parameter uncertainty (e.g., oscillatory dynamics); analysis revealed that five parameters were highly influential in these dynamics. Overall, we demonstrate feasibility of performing comprehensive UQ/SA for cardiac cell models and demonstrate how to assess robustness and overcome model failure when performing cardiac UQ analyses. The approach presented here represents an important and significant step toward the development of model-based clinical tools which are demonstrably robust to all underlying uncertainties and therefore more reliable in safety-critical decision-making.

This paper presents an algorithm for efficient uncertainty quantification (UQ) in the presence of many uncertainties that follow a nonstandard distribution (e.g., lognormal). Using the polynomial chaos expansion (PCE), the algorithm builds surrogate models of uncertainty as functions of a standard distribution (e.g., Gaussian variables). The key to build these surrogate models is to calculate PCE coefficients of model outputs, which is computationally challenging, especially when dealing with models defined by complex functions (e.g., nonpolynomial terms) under many uncertainties. To address this issue, an algorithm that integrates the PCE with the generalized dimension reduction method (gDRM) is utilized to convert the high-dimensional integrals, required to calculate the PCE coefficients of model predictions, into several lower-dimensional ones that can be rapidly solved with quadrature rules. The accuracy of the algorithm is validated with four examples in structural reliability analysis and compared to other existing techniques, such as Monte Carlo simulations and the least angle regression-based PCE. Our results show our algorithm provides accurate UQ results and is computationally efficient when dealing with many uncertainties, thus laying the foundation to address UQ in complex control systems.

In this work we propose an approach for accelerating Uncertainty Quantification (UQ) analysis in the context of Multifidelity applications. In the presence of complex multiphysics applications, which often require a prohibitive computational cost for each evaluation, mul- tifidelity UQ techniques try to accelerate the convergence of statistics by leveraging the in- formation collected from a larger number of a lower fidelity model realizations. However, at the-state-of-the-art, the performance of virtually all the multifidelity UQ techniques is related to the correlation between the high and low-fidelity models. In this work we proposed to design a multifidelity UQ framework based on the identification of independent important directions for each model. The main idea is that if the responses of each model can be represented in a common space, this latter can be shared to enhance the correlation when the samples are drawn with respect to it instead of the original variables. There are also two main additional advantages that follow from this approach. First, the models might be correlated even if their original parametrizations are chosen independently. Second, if the shared space between mod- els has a lower dimensionality than the original spaces, the UQ analysis might benefit from a dimension reduction standpoint. In this work we designed this general framework and we also tested it on several test problems ranging from analytical functions for verification purpose, up to more challenging application problems as an aero-thermo-structural analysis and a scramjet flow analysis.