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

ABSTRACTPROSAIL is a combination of the leaf optical properties spectra (PROSPECT) model and the scattering by arbitrarily inclined leaves (SAIL) canopy bidirectional reflectance model. When modelling forest canopy reflectance using the PROSAIL radiative transfer model, the sensitivities of parameters can affect the modelling accuracy. Traditionally, sensitivities have been assessed using local sensitivity analysis (LSA); however, drawbacks to this approach include a lack of consideration for coupled effects between different parameters. In this study, parameter sensitivities in the PROSAIL model were calculated using two global sensitivity analysis (GSA) methods (the Extended Fourier Amplitude Sensitivity Test (EFAST) method and the Morris method), field measurements, and Landsat 5 Thematic Mapper (TM) data for a Moso bamboo forest. The results of GSA were compared with those of LSA in order to identify the key parameters impacting the Moso bamboo forest canopy reflectance, and to provide a reference for model optimization and vegetation canopy inversion improvement. The results showed that: (1) the sensitivities of six major input parameters of the PROSAIL model were generally consistent with the sorting orders of the two GSA methods, but were not in accordance with those from the LSA method, especially in the mid-infrared band; (2) coupled effects among parameters acting on reflectance simulation in visible light bands were greater than those in infrared bands; (3) the simulated canopy reflectance was evaluated using Landsat 5 TM data, and the results simulated based on LSA analysis showed higher error than those based on GSA analysis, because the LSA method ignored the influence of some parameters on canopy reflectance, e.g. leaf mesophyll structure (N), average leaf angle (ALA), leaf water content (Cw), and leaf dry matter content (Cm). However, GSA was able to fully consider the coupled effects among parameters, and thus identified the sensitive parameters impacting on reflectance more accurately.

In this paper, we study the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana during its initial phase by using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, ℛ0, for the proposed model is 1.04. One of the main focus of this study is global stability results. Theoretically and numerically, we show that the disease persistence depends on ℛ0. We carry out a local and global sensitivity analysis. The local sensitivity analysis shows that the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility rate from the infectious with delayed diagnosis to the susceptible individuals. And that the most negative sensitive parameters are: self-quarantined, waiting time of the infectious for delayed diagnosis and the proportion of the infectious with timely diagnosis. The global sensitivity analysis using the partial rank correlation coefficient confirms the directional flow of the local sensitivity analysis. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection). Other recommendations for controlling the disease from the proposed model are provided in Section 7.

Global Sensitivity Analysis of Arrhythmic Risk Biomarkers in Cardiac Single Cell Models

There is uncertainty in the results of any mathematical model due to different reasons. It is important to estimate this uncertainty. Sensitivity analysis is commonly used to estimate how the changes in the input parameters affect the solutions of the model. In this paper, we discuss different ways of performing local and global sensitivity analyses and apply them to two models: an epidemic model and a new myocardial infarction model, both based on ordinary differential equations. The first model is a simple model used to explain the ideas, while the second one shows how to apply them to a model with more state variables and parameters. We find that if the parameters are not accurately known, local sensitivity analysis can be misleading and that global sensitivity methods that sample the whole parameter space, varying all the values of the parameters at the same time, are the most reliable. We also show how the sensitivity analysis results can be used to determine the uncertainty in the results of the model. We present numerical simulations.

Sensitivity analyses are frequently used during the design of engineering systems to qualify and quantify the effect of parametric variation in the performance of a system. Two primary types of sensitivity analyses are generally used: local and global. Local analyses, generally involving derivative-based measures, have a significantly lower computational burden than global analyses but only provide measures of sensitivity around a nominal point. Global analyses, generally performed with a Monte Carlo sampling approach, and variation-based measures provide a complete description of sensitivity but incur a large computational burden and require information regarding the distributions of the design parameters in a concept. Local analyses are generally suited to the early stages of design when parametric information is limited, and a large number of concepts must be evaluated (necessitating a light computational burden). Global analyses are more suited to the later stages of design when more information about parametric distributions is available and fewer concepts are under consideration. Current derivative-based local approaches provide a different and incompatible set of measures than a global variation-based analysis. This makes a direct comparison of local to global measures ill posed. To reconcile local and global sensitivity analyses, a hybrid local variation-based sensitivity (HyVar) approach is presented. This approach has a similar computational burden to a local approach but produces measures or percentage contributions. The HyVar approach is directly comparable to global variation-based approaches. In this paper, the HyVar sensitivity analysis method is developed in the context of a functional based behavioral modeling framework. An example application of the method is presented along with a summary of results produced from a more comprehensive example.

Bayesian parameter and joint probability distribution estimation for a hysteretic constitutive model of reinforcing steel

Efficient global sensitivity analysis for flow-induced vibration of a nuclear reactor assembly using Kriging surrogates

Parametric sensitivity analysis (SA) is an essential tool in optical data analysis aiming to quantify the relative importance of optical model parameters and identify those with a low influence which should remain fixed during analysis in order to simplify a model. Typically, such sensitivity studies are performed using a local sensitivity analysis, also referred to as “one-at-a-time” analysis, which estimates parameter sensitivity by evaluating the changes in model output while perturbing one parameter at a time and holding all other parameters fixed. All the pitfalls of the local sensitivity approach are quite obvious and well known; however, local SA is still prevailing in the area of data analysis for spectroscopic ellipsometry. In this study, we discuss applications of a global qualitative analysis introduced by Morris in 1991 which determines an overall significance for each model parameter and describes its nonlinear effect on model’s output and/or interactions with other parameters. The Morris method allows effective separation of the model parameters into different groups such as parameters with negligible effects, parameters with large linear effects without interactions, and parameters with large nonlinear and/or interaction effects. Here, we carried out the Morris sensitivity analysis to reveal the model parameter significance ranking in a test case of the B-spline model for titanium nitride (TiN). Such a screening approach can be considered as a practical tool for the initial global SA strategy prior to true “all-at-a-time” global sensitivity analysis.

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

Global sensitivity analysis and uncertainty quantification of soot formation in an n-dodecane spray flame

Equationing Arabica coffee: Adaptation, calibration, and application of an agrometeorological model for yield estimation

Reservoir history matching by ensemble smoother with principle component and sensitivity analysis for heterogeneous formations

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.

Parameter estimation is a major challenge for mathematical modelling of biological systems. Given the uncertainties associated with model parameters, it is important to understand how sensitive the model output is to variations in parameter values. A local sensitivity analysis determines the model sensitivity to parameter variations over a localised region around the nominal parameter values, whereas a global sensitivity analysis (GSA) investigates the sensitivity over the entire parameter space. Using a T-cell receptor-activated Erk-MAPK signalling pathway model as an example, the authors present a comparative study of a variety of different sensitivity analysis techniques. These techniques include: local sensitivity analysis, existing GSA methods of partial rank correlation coefficient, Sobol's, extended Fourier amplitude sensitivity test, as well as a weighted average of local sensitivities and a new GSA method to extract global parameter sensitivities from a parameter identification routine. Results of this study revealed critical reactions in the signalling pathway and their impact on the signalling dynamics and provided insights into embedded regulatory mechanisms such as feedback loops in the pathway. From this study, a recommendation emerges for a general sensitivity analysis strategy to efficiently and reliably infer quantitative, dynamic as well as topological properties from systems biology models.

Global sensitivity analysis in high dimensions with PLS-PCE