Dimensionality reduction for surrogate model construction for global sensitivity analysis: Comparison between active subspace and local sensitivity analysis

2021 ◽  
Vol 232 ◽  
pp. 111501
Author(s):  
Keli Lin ◽  
Zijun Zhou ◽  
Chung K. Law ◽  
Bin Yang
Keyword(s):  
Sensitivity Analysis ◽  
Dimensionality Reduction ◽  
Surrogate Model ◽  
Global Sensitivity Analysis ◽  
Model Construction ◽  
Local Sensitivity ◽  
Local Sensitivity Analysis ◽  
Global Sensitivity ◽  
Active Subspace

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.

scholarly journals A Global Sensitivity Analysis Framework for Hybrid Simulation with Stochastic Substructures

2021 ◽  
Vol 7 ◽  
Author(s):  
Nikolaos Tsokanas ◽  
Xujia Zhu ◽  
Giuseppe Abbiati ◽  
Stefano Marelli ◽  
Bruno Sudret ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Hybrid Model ◽  
Surrogate Model ◽  
Global Sensitivity Analysis ◽  
Hybrid Simulation ◽  
Hybrid Models ◽  
Analysis Framework ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Realistic Situation

Hybrid simulation is an experimental method used to investigate the dynamic response of a reference prototype structure by decomposing it to physically-tested and numerically-simulated substructures. The latter substructures interact with each other in a real-time feedback loop and their coupling forms the hybrid model. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic, as nominally identical specimens are, in practice, never actually identical. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol’ sensitivity indices are computed for substructure quantity of interest response quantiles. Normally, several repetitions of every single sample of the inputs parameters would be required to replicate the response of a stochastic hybrid model. In this regard, a great advantage of the proposed framework is that the generalized lambda surrogate model does not require repeated evaluations of the same sample. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.

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 Morris method with improved sampling strategy and Sobol’ Variance-based method, as validation tool on Numerical Model of Richard’s Equation

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Sunny Goh
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Scheme ◽  
Sampling Strategy ◽  
Manhattan Distance ◽  
Total Output ◽  
Local Sensitivity ◽  
Local Sensitivity Analysis ◽  
Global Sensitivity ◽  
Morris Method ◽  
Richard's Equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at  and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters  and  is suggesting a greater significant digits is required to reduce its input uncertainty range.

scholarly journals Moment-based metrics for global sensitivity analysis of hydrological systems

2017 ◽  
Vol 21 (12) ◽  
pp. 6219-6234 ◽  
Author(s):  
Aronne Dell'Oca ◽  
Monica Riva ◽  
Alberto Guadagnini
Keyword(s):  
Sensitivity Analysis ◽  
Surrogate Model ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Original System ◽  
Model Complexity ◽  
Model Output ◽  
Global Sensitivity ◽  
Reduction Techniques ◽  
The Impact

Abstract. We propose new metrics to assist global sensitivity analysis, GSA, of hydrological and Earth systems. Our approach allows assessing the impact of uncertain parameters on main features of the probability density function, pdf, of a target model output, y. These include the expected value of y, the spread around the mean and the degree of symmetry and tailedness of the pdf of y. Since reliable assessment of higher-order statistical moments can be computationally demanding, we couple our GSA approach with a surrogate model, approximating the full model response at a reduced computational cost. Here, we consider the generalized polynomial chaos expansion (gPCE), other model reduction techniques being fully compatible with our theoretical framework. We demonstrate our approach through three test cases, including an analytical benchmark, a simplified scenario mimicking pumping in a coastal aquifer and a laboratory-scale conservative transport experiment. Our results allow ascertaining which parameters can impact some moments of the model output pdf while being uninfluential to others. We also investigate the error associated with the evaluation of our sensitivity metrics by replacing the original system model through a gPCE. Our results indicate that the construction of a surrogate model with increasing level of accuracy might be required depending on the statistical moment considered in the GSA. The approach is fully compatible with (and can assist the development of) analysis techniques employed in the context of reduction of model complexity, model calibration, design of experiment, uncertainty quantification and risk assessment.

scholarly journals Morris method with improved sampling strategy and Sobol’ variance-based method, as validation tool on numerical model of Richard’s equation

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Sunny Goh
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Scheme ◽  
Sampling Strategy ◽  
Manhattan Distance ◽  
Total Output ◽  
Local Sensitivity ◽  
Local Sensitivity Analysis ◽  
Global Sensitivity ◽  
Morris Method ◽  
Richard's Equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at  and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters  and  is suggesting a greater significant digits is required to reduce its input uncertainty range.

scholarly journals Morris method with improved sampling strategy and Sobol’ variance-based method, as validation tool on numerical model of Richard’s equation

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Sunny Goh
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Scheme ◽  
Sampling Strategy ◽  
Manhattan Distance ◽  
Total Output ◽  
Local Sensitivity ◽  
Local Sensitivity Analysis ◽  
Global Sensitivity ◽  
Morris Method ◽  
Richard's Equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at  and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters  and  is suggesting a greater significant digits is required to reduce its input uncertainty range.

scholarly journals Global sensitivity analysis and adaptive stochastic sampling of a subsurface-flow model using active subspaces

2019 ◽  
Vol 23 (9) ◽  
pp. 3787-3805 ◽  
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 modeling 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 as to 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 parameters, 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 meaningfully be done with second-order polynomials.

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