scholarly journals Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active subspaces

2020 ◽  
Vol 34 (11) ◽  
pp. 1813-1830
Author(s):  
Daniel Erdal ◽  
Sinan Xiao ◽  
Wolfgang Nowak ◽  
Olaf A. Cirpka
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Process ◽  
Parameter Space ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Large Sample Size ◽  
Global Sensitivity ◽  
Environmental Models ◽  
Additional Costs ◽  
Active Subspace

Abstract Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70–90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs.

scholarly journals Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling

2021 ◽  
Author(s):  
Sebastian Brandstaeter ◽  
Sebastian L. Fuchs ◽  
Jonas Biehler ◽  
Roland C. Aydin ◽  
Wolfgang A. Wall ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Computational Studies ◽  
Growth And Remodeling ◽  
Global Sensitivity ◽  
Output Variability ◽  
Constrained Mixture ◽  
The One ◽  
Influential Parameters

AbstractGrowth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

scholarly journals Global Sensitivity Analysis and Adaptive Stochastic Sampling of a Subsurface-Flow Model Using Active Subspaces

2019 ◽  
Author(s):  
Daniel Erdal ◽  
Olaf A. Cirpka
Keyword(s):  
Sensitivity Analysis ◽  
Flow Model ◽  
Global Sensitivity Analysis ◽  
Subsurface Flow ◽  
Full Model ◽  
Stochastic Sampling ◽  
Global Sensitivity ◽  
Parameter Combination ◽  
Active Subspaces ◽  
Active Subspace

Abstract. Integrated hydrological modelling of domains with complex subsurface features requires many highly uncertain parameters. Performing a global uncertainty analysis using an ensemble of model runs can help bring clarity which of these parameters really influence system behavior, and for which high parameter uncertainty does not result in similarly high uncertainty of model predictions. However, already creating a sufficiently large ensemble of model simulation for the global sensitivity analysis can be challenging, as many combinations of model parameters can lead to unrealistic model behavior. In this work we use the method of active subspaces to perform a global sensitivity analysis. While building-up the ensemble, we use the already existing ensemble members to construct low-order meta-models based on the first two active subspace dimensions. The meta-models are used to pre-determine whether a random parameter combination in the stochastic sampling is likely to result in unrealistic behavior, so that such a parameter combination is excluded without running the computationally expensive full model. An important reason for choosing the active subspace method is that both the activity score of the global sensitivity analysis and the meta-models can easily be understood and visualized. We test the approach on a subsurface flow model including uncertain hydraulic parameter, uncertain boundary conditions, and uncertain geological structure. We show that sufficiently detailed active subspaces exist for most observations of interest. The pre-selection by the meta-model significantly reduces the number of full model runs that must be rejected due to unrealistic behavior. An essential but difficult part in active subspace sampling using complex models is approximating the gradient of the simulated observation with respect to all parameters. We show that this can effectively and meaningful be done with second-order polynomials.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Comprehensive global sensitivity analysis of a repository model using different types of transformations and metamodeling techniques

2021 ◽  
Author(s):  
Sabine M. Spiessl ◽  
Dirk-A. Becker ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Higher Order ◽  
Model Parameters ◽  
High Dimensional Model Representation ◽  
Model Output ◽  
Global Sensitivity ◽  
Sparse Polynomial ◽  
Sensitivity Indices ◽  
Highly Nonlinear

<p>Due to their highly nonlinear, non-monotonic or even discontinuous behavior, sensitivity analysis of final repository models can be a demanding task. Most of the output of repository models is typically distributed over several orders of magnitude and highly skewed. Many values of a probabilistic investigation are very low or even zero. Although this is desirable in view of repository safety it can distort the evidence of sensitivity analysis. For the safety assessment of the system, the highest values of outputs are mainly essential and if those are only a few, their dependence on specific parameters may appear insignificant. By applying a transformation, different model output values are differently weighed, according to their magnitude, in sensitivity analysis. Probabilistic methods of higher-order sensitivity analysis, applied on appropriately transformed model output values, provide a possibility for more robust identification of relevant parameters and their interactions. This type of sensitivity analysis is typically done by decomposing the total unconditional variance of the model output into partial variances corresponding to different terms in the ANOVA decomposition. From this, sensitivity indices of increasing order can be computed. The key indices used most often are the first-order index (SI1) and the total-order index (SIT). SI1 refers to the individual impact of one parameter on the model and SIT represents the total effect of one parameter on the output in interactions with all other parameters. The second-order sensitivity indices (SI2) describe the interactions between two model parameters.</p><p>In this work global sensitivity analysis has been performed with three different kinds of output transformations (log, shifted and Box-Cox transformation) and two metamodeling approaches, namely the Random-Sampling High Dimensional Model Representation (RS-HDMR) [1] and the Bayesian Sparse PCE (BSPCE) [2] approaches. Both approaches are implemented in the SobolGSA software [3, 4] which was used in this work. We analyzed the time-dependent output with two approaches for sensitivity analysis, i.e., the pointwise and generalized approaches. With the pointwise approach, the output at each time step is analyzed independently. The generalized approach considers averaged output contributions at all previous time steps in the analysis of the current step. Obtained results indicate that robustness can be improved by using appropriate transformations and choice of coefficients for the transformation and the metamodel.</p><p>[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.</p><p>[2] Q. Shao, A. Younes, M. Fahs, T.A. Mara (2017). Bayesian sparse polynomial chaos expansion for global sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 318: 474-496.</p><p>[3] S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus (2018). Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004.</p><p>[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.</p>

scholarly journals Global sensitivity analysis, probabilistic calibration, and predictive assessment for the Data Assimilation Linked Ecosystem Carbon model

2014 ◽  
Vol 7 (5) ◽  
pp. 6893-6948
Author(s):  
C. Safta ◽  
D. Ricciuto ◽  
K. Sargsyan ◽  
B. Debusschere ◽  
H. N. Najm ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Data Assimilation ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Forest Site ◽  
Carbon Cycle Model ◽  
Global Sensitivity ◽  
Predictive Skill ◽  
Ecosystem Carbon

Abstract. In this paper we propose a probabilistic framework for an uncertainty quantification study of a carbon cycle model. A Global Sensitivity Analysis (GSA) study indicates the parameters and parameter couplings that are important at different times of the year for Quantities of Interest obtained with the Data Assimilation Linked Ecosystem Carbon (DALEC) model. We then employ a Bayesian approach to calibrate the parameters of DALEC using net ecosystem exchange observations at the Harvard Forest site. The calibration exercise is guided by GSA and by Fisher information matrix results that quantify the amount of information carried by the experimental data about specific model parameters. The calibration results are employed in the second part of the paper to assess the predictive skill of the model via posterior predictive checks. These checks show a better performance for the non-steady state model during the growing season compared to the one employing steady state assumptions. Overall, this study leads to a 40% improvement in the predictive skill of DALEC and highlights the importance of considering correlations in the model parameters as informed by the data.

Sensitivity analysis and the challenges posed by multiple approaches: a multifaceted mess

2020 ◽  
Author(s):  
Monica Riva ◽  
Aronne Dell'Oca ◽  
Alberto Guadagnini
Keyword(s):  
Sensitivity Analysis ◽  
Model Calibration ◽  
Global Sensitivity Analysis ◽  
System Model ◽  
Model Parameters ◽  
Model Output ◽  
Multiple Model ◽  
Total Uncertainty ◽  
Global Sensitivity ◽  
Sensitivity Indices

<p>Modern models of environmental and industrial systems have reached a relatively high level of complexity. The latter aspect could hamper an unambiguous understanding of the functioning of a model, i.e., how it drives relationships and dependencies among inputs and outputs of interest. Sensitivity Analysis tools can be employed to examine this issue.</p><p>Global sensitivity analysis (GSA) approaches rest on the evaluation of sensitivity across the entire support within which system model parameters are supposed to vary. In this broad context, it is important to note that the definition of a sensitivity metric must be linked to the nature of the question(s) the GSA is meant to address. These include, for example: (i) which are the most important model parameters with respect to given model output(s)?; (ii) could we set some parameter(s) (thus assisting model calibration) at prescribed value(s) without significantly affecting model results?; (iii) at which space/time locations can one expect the highest sensitivity of model output(s) to model parameters and/or knowledge of which parameter(s) could be most beneficial for model calibration?</p><p>The variance-based Sobol’ Indices (e.g., Sobol, 2001) represent one of the most widespread GSA metrics, quantifying the average reduction in the variance of a model output stemming from knowledge of the input. Amongst other techniques, Dell’Oca et al. [2017] proposed a moment-based GSA approach which enables one to quantify the influence of uncertain model parameters on the (statistical) moments of a target model output.</p><p>Here, we embed in these sensitivity indices the effect of uncertainties both in the system model conceptualization and in the ensuing model(s) parameters. The study is grounded on the observation that physical processes and natural systems within which they take place are complex, rendering target state variables amenable to multiple interpretations and mathematical descriptions. As such, predictions and uncertainty analyses based on a single model formulation can result in statistical bias and possible misrepresentation of the total uncertainty, thus justifying the assessment of multiple model system conceptualizations. We then introduce copula-based sensitivity metrics which allow characterizing the global (with respect to the input) value of the sensitivity and the degree of variability (across the whole range of the input values) of the sensitivity for each value that the prescribed model output can possibly undertake, as driven by a governing model. In this sense, such an approach to sensitivity is global with respect to model input(s) and local with respect to model output, thus enabling one to discriminate the relevance of an input across the entire range of values of the modeling goal of interest. The methodology is demonstrated in the context of flow and reactive transport scenarios.</p><p> </p><p><strong>References</strong></p><p>Sobol, I. M., 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Sim., 55, 271-280.</p><p>Dell’Oca, A., Riva, M., Guadagnini, A., 2017. Moment-based metrics for global sensitivity analysis of hydrological systems. Hydr. Earth Syst. Sci., 21, 6219-6234.</p>

scholarly journals Global Sensitivity Analysis of Parameter Uncertainty in Landscape Evolution Models

2017 ◽  
Author(s):  
Christopher J. Skinner ◽  
Tom J. Coulthard ◽  
Wolfgang Schwanghart ◽  
Marco J. Van De Wiel ◽  
Greg Hancock
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Global Sensitivity Analysis ◽  
Landscape Evolution ◽  
Sensitivity Analyses ◽  
Large Set ◽  
Sediment Yields ◽  
Global Sensitivity ◽  
Environmental Models ◽  
Morris Method

Abstract. Landscape Evolution Models have a long history of use as exploratory models, providing greater understanding of the role large scale processes have on the long-term development of the Earth’s surface. As computational power has advanced so has the development and sophistication of these models. This has seen them applied at increasingly smaller scale and shorter-term simulations at greater detail. However, this has not gone hand-in-hand with more rigorous verifications that are commonplace in the applications of other types of environmental models- for example Sensitivity Analyses. This can be attributed to a paucity of data and methods available in order to calibrate, validate and verify the models, and also to the extra complexity Landscape Evolution Models represent – without these it is not possible to produce a reliable Objective Function against which model performance can be judged. To overcome this deficiency, we present a set of Model Functions – each representing an aspect of model behaviour – and use these to assess the relative sensitivity of a Landscape Evolution Model (CAESAR-Lisflood) to a large set of parameters via a global Sensitivity Analysis using the Morris Method. This novel combination of behavioural Model Functions and the Morris Method provides insight into which parameters are the greatest source of uncertainty in the model, and which have the greatest influence over different model behaviours. The method was repeated over two different catchments, showing that across both catchments and across most model behaviours the choice of Sediment Transport formula was the dominate source of uncertainty in the CAESAR-Lisflood model, although there were some differences between the two catchments. Crucially, different parameters influenced the model behaviours in different ways, with Model Functions related to internal geomorphic changes responding in different ways to those related to sediment yields from the catchment outlet. This method of behavioural sensitivity analysis provides a useful method of assessing the performance of Landscape Evolution Models in the absence of data and methods for an Objective Function approach.

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