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1. Global sensitivity analysis of fractional-order viscoelasticity model

   Miles, P.R. (June 2019, SPIE Smart Structures + Nondestructive Evaluation)

   In this paper, we investigate hyperelastic and viscoelastic model parameters using Global Sensitivity Analysis(GSA). These models are used to characterize the physical response of many soft-elastomers, which are used in a wide variety of smart material applications. Recent research has shown the effectiveness of using fractional-order calculus operators in modeling the viscoelastic response. The GSA is performed using parameter subset selection (PSS), which quantifies the relative parameter contributions to the linear and nonlinear, fractional-order viscoelastic models. Calibration has been performed to quantify the model parameter uncertainty; however, this analysis has led to questions regarding parameter sensitivity and whether or not the parameters can be uniquely identified given the available data. By performing GSA we can determine which parameters are most influential in the model, and fix non-influential parameters at a nominal value. The model calibration can then be performed to quantify the uncertainty of the influential parameters. 

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2. A machine learning approach to emulation and biophysical parameter estimation with the Community Land Model, version 5

   https://doi.org/10.5194/ascmo-6-223-2020  

   Dagon, Katherine; Sanderson, Benjamin M.; Fisher, Rosie A.; Lawrence, David M. (January 2020, Advances in Statistical Climatology, Meteorology and Oceanography)

   null (Ed.)

   Abstract. Land models are essential tools for understanding and predicting terrestrial processes and climate–carbon feedbacks in the Earth system, but uncertainties in their future projections are poorly understood. Improvements in physical process realism and the representation of human influence arguably make models more comparable to reality but also increase the degrees of freedom in model configuration, leading to increased parametric uncertainty in projections. In this work we design and implement a machine learning approach to globally calibrate a subset of the parameters of the Community Land Model, version 5 (CLM5) to observations of carbon and water fluxes. We focus on parameters controlling biophysical features such as surface energy balance, hydrology, and carbon uptake. We first use parameter sensitivity simulations and a combination of objective metrics including ranked global mean sensitivity to multiple output variables and non-overlapping spatial pattern responses between parameters to narrow the parameter space and determine a subset of important CLM5 biophysical parameters for further analysis. Using a perturbed parameter ensemble, we then train a series of artificial feed-forward neural networks to emulate CLM5 output given parameter values as input. We use annual mean globally aggregated spatial variability in carbon and water fluxes as our emulation and calibration targets. Validation and out-of-sample tests are used to assess the predictive skill of the networks, and we utilize permutation feature importance and partial dependence methods to better interpret the results. The trained networks are then used to estimate global optimal parameter values with greater computational efficiency than achieved by hand tuning efforts and increased spatial scale relative to previous studies optimizing at a single site. By developing this methodology, our framework can help quantify the contribution of parameter uncertainty to overall uncertainty in land model projections. 

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3. Iterative Global Sensitivity Analysis Algorithm with Neural Network Surrogate Modeling

   https://doi.org/10.1007/978-3-030-77970-2_23  

   Liu, Y.C.; Nagawkar, J.; Leifsson, L.; Koziel, S.; Pietrenko-Dabrowska, A. (June 2021, Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science)

   Paszynski, M.; Kranzlmüller, D.; Krzhizhanovskaya, V.V.; Dongarra, J.J.; Sloot, P.M. (Ed.)

   Global sensitivity analysis (GSA) is a method to quantify the effect of the input parameters on outputs of physics-based systems. Performing GSA can be challenging due to the combined effect of the high computational cost of each individual physics-based model, a large number of input parameters, and the need to perform repetitive model evaluations. To reduce this cost, neural networks (NNs) are used to replace the expensive physics-based model in this work. This introduces the additional challenge of finding the minimum number of training data samples required to train the NNs accurately. In this work, a new method is introduced to accurately quantify the GSA values by iterating over both the number of samples required to train the NNs, terminated using an outer-loop sensitivity convergence criteria, and the number of model responses required to calculate the GSA, terminated with an inner-loop sensitivity convergence criteria. The iterative surrogate-based GSA guarantees converged values for the Sobol’ indices and, at the same time, alleviates the specification of arbitrary accuracy metrics for the surrogate model. The proposed method is demonstrated in two cases, namely, an eight-variable borehole function and a three-variable nondestructive testing (NDT) case. For the borehole function, both the first- and total-order Sobol’ indices required 200 and 105 data points to terminate on the outer- and inner-loop sensitivity convergence criteria, respectively. For the NDT case, these values were 100 for both first- and total-order indices for the outer-loop sensitivity convergence, and 106 and 103 for the inner-loop sensitivity convergence, respectively, for the first- and total-order indices, on the inner-loop sensitivity convergence. The differences of the proposed method with GSA on the true functions are less than 3% in the analytical case and less than 10% in the physics-based case (where the large error comes from small Sobol’ indices). 

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4. An integrated framework of global sensitivity analysis and calibration for spatially explicit agent‐based models

   https://doi.org/10.1111/tgis.12837  

   Kang, Jeon‐Young; Michels, Alexander; Crooks, Andrew; Aldstadt, Jared; Wang, Shaowen (September 2021, Transactions in GIS)

   Abstract Calibration of agent‐based models (ABMs) is a major challenge due to the complex nature of the systems being modeled, the heterogeneous nature of geographical regions, the varying effects of model inputs on the outputs, and computational intensity. Nevertheless, ABMs need to be carefully tuned to achieve the desirable goal of simulating spatiotemporal phenomena of interest, and a well‐calibrated model is expected to achieve an improved understanding of the phenomena. To address some of the above challenges, this article proposes an integrated framework of global sensitivity analysis (GSA) and calibration, called GSA‐CAL. Specifically, variance‐based GSA is applied to identify input parameters with less influence on differences between simulated outputs and observations. By dropping these less influential input parameters in the calibration process, this research reduces the computational intensity of calibration. Since GSA requires many simulation runs, due to ABMs' stochasticity, we leverage the high‐performance computing power provided by the advanced cyberinfrastructure. A spatially explicit ABM of influenza transmission is used as the case study to demonstrate the utility of the framework. Leveraging GSA, we were able to exclude less influential parameters in the model calibration process and demonstrate the importance of revising local settings for an epidemic pattern in an outbreak. 

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5. Global Sensitivity Analysis and Uncertainty Quantification for Background Solar Wind Using the Alfvén Wave Solar Atmosphere Model

   https://doi.org/10.1029/2022SW003262  

   Jivani, Aniket; Sachdeva, Nishtha; Huang, Zhenguang; Chen, Yang; van der Holst, Bart; Manchester, Ward; Iong, Daniel; Chen, Hongfan; Zou, Shasha; Huan, Xun; et al (January 2023, Space Weather)

   Abstract Modeling the impact of space weather events such as coronal mass ejections (CMEs) is crucial to protecting critical infrastructure. The Space Weather Modeling Framework is a state‐of‐the‐art framework that offers full Sun‐to‐Earth simulations by computing the background solar wind, CME propagation, and magnetospheric impact. However, reliable long‐term predictions of CME events require uncertainty quantification (UQ) and data assimilation. We take the first steps by performing global sensitivity analysis (GSA) and UQ for background solar wind simulations produced by the Alfvén Wave Solar atmosphere Model (AWSoM) for two Carrington rotations: CR2152 (solar maximum) and CR2208 (solar minimum). We conduct GSA by computing Sobol' indices that quantify contributions from model parameter uncertainty to the variance of solar wind speed and density at 1 au, both crucial quantities for CME propagation and strength. Sobol' indices also allow us to rank and retain only the most important parameters, which aids in the construction of smaller ensembles for the reduced‐dimension parameter space. We present an efficient procedure for computing the Sobol' indices using polynomial chaos expansion surrogates and space‐filling designs. The PCEs further enable inexpensive forward UQ. Overall, we identify three important model parameters: the multiplicative factor applied to the magnetogram, Poynting flux per magnetic field strength constant used at the inner boundary, and the coefficient of the perpendicular correlation length in the turbulent cascade model in AWSoM. 

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