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This study aimed to design a linear feedback control approach for a parametrically excited energy harvesting system utilizing a piezoelectric material as the transduction element. The purpose was to significantly increase the amount of energy produced compared to that produced by the original system. To do so, firstly, it is necessary to analyze the stability of the system and perform a global sensitivity analysis to determine the physical parameters of the system that most contribute to energy production. The sensitivity analysis is done by calculating the Sobol indices, which are statistical indices that measure the relative contribution of each input variable (in this case, the physical parameters of the system) to the contribution of all input variables. In the stability analysis, the state transition matrix approximation techniques created by Sinha and Butcher and the results of the Floquet Theory for periodic systems were used. Stability analysis and global sensitivity analysis are methodologically complementary techniques for a better understanding of the dynamics of a system. In the case of this work, they are applied to an energy-harvesting system based on mechanical vibrations, providing important information to design a more efficient controller. The control technique used was proposed by Sinha and Butcher (1997), and is known as Linear Feedback Controller Design via the Lyapunov-Floquet Transform.

Background: Whole-genome models (GEMs) have become a versatile tool for systems biology, biotechnology, and medicine. GEMs created by automatic and semi-automatic approaches contain a lot of redundant reactions. At the same time, the nonlinearity of the model makes it difficult to evaluate the significance of the reaction for cell growth or metabolite production. Methods: We propose a new way to apply the global sensitivity analysis (GSA) to GEMs in a straightforward parallelizable fashion. Results: We have shown that Partial Rank Correlation Coefficient (PRCC) captures key steps in the metabolic network despite the network distance from the product synthesis reaction. Conclusions: FBA-PRCC is a fast, interpretable, and reliable metric to identify the sign and magnitude of the reaction contribution to various cellular functions.

Polyurea (PUA) elastomers are extensively used in a wide range of applications spanning from biomedical to defense fields due to their enabling mechanical properties. These materials can be further reinforced through the incorporation of nanoparticles to form nanocomposites. This study focuses on an IPDI‐based (isophorone diisocyanate) PUA matrix with exfoliated graphene nanoplatelet (xGnP) fillers. We propose a generalized‐order constitutive model by combining one Fractional Maxwell Model (FMM) and one Fractional Maxwell Gel (FMG) branch in a parallel configuration. This has been accomplished via introducing a new dimensionless number that bridges between these branches physically and mathematically. This model exhibits a maximum relative error of less than 2% when validated against the experimental master curves across more than ten decades of shifted frequency, demonstrating its robustness and accuracy. Through our systematic local and global (variance‐based) sensitivity analyses, we further investigate the behavior of the nanocomposites, leading to a priority list of model parameters in the order of their contribution to model uncertainty/sensitivity. The main contribution of the present study is to develop a robust and efficient framework to construct the most parsimonious constitutive models from data with a high degree of physical interpretability and generality of use in a range of applications. In this study, we proposed a new fractional‐order model for viscoelasticity in Polyurea‐Graphene nanocomposites in addition to the introduction of a new dimensionless number connecting fractional Maxwell branches to composite polymer morphology. Furthermore, we conducted a systematic local‐to‐global sensitivity analysis on the constitutive models to objectively identify a consistent set of most and least influential model parameters leading to the dimensionality reduction of models.

Surrogate models are popular tool to approximate the functional relationship of expensive simulation models in multiple scientific and engineering disciplines. Successful use of surrogate models can provide significant savings of computational cost. However, with a variety of surrogate model approaches available in literature, it is a difficult task to select an appropriate one at hand. In this paper, we present an overview of surrogate model approaches with an emphasis of their application for variance-based global sensitivity analysis, including polynomial regression model, high-dimensional model representation, state-dependent parameter, polynomial chaos expansion, Kriging/Gaussian Process, support vector regression, radial basis function, and low rank tensor approximation. The accuracy and efficiency of these approaches are compared with several benchmark examples. The strengths and weaknesses of these surrogate models are discussed, and the recommendations are provided for different types of applications. For ease of implementations, the packages, as well as toolboxes, of surrogate model techniques and their applications for global sensitivity analysis are collected.

In the process of parameter identification, sensitivity analysis is mainly used to determine key parameters with high sensitivity in the model. Sensitivity analysis methods include local sensitivity analysis (LSA) and global sensitivity analysis (GSA). The LSA method has been widely used for power system parameter identification for a long time, while the GSA has started to be used in recent years. However, there is no clear conclusion on the impact of different sensitivity analysis methods on parameter identification results. Therefore, this paper compares and studies the roles that LSA and GSA can play in different parameter identification methods, providing clear guidance for the selection of sensitivity analysis methods and parameter identification methods. The conclusion is as follows. If the identification strategy that only identifies key parameters with high sensitivity is adopted, we recommend still using the existing LSA method. If using a groupwise alternating identification strategy (GAIS) for high- and low-sensitivity parameters, either LSA or GSA can be used. To improve the identification accuracy, it is more important to improve the identification strategy than to change the sensitivity analysis method. When the accuracy of the non-key parameters with low sensitivity cannot be confirmed, using the GAIS is an effective method for ensuring identification accuracy. In addition, it should be noted that the high sensitivity of a parameter does not necessarily mean that the parameter is identifiable, which is revealed by the examples used in this paper.

Power systems are increasingly affected by various sources of uncertainty at all levels. The investigation of their effects thus becomes a critical challenge for their design and operation. Sensitivity Analysis (SA) can be instrumental for understanding the origins of system uncertainty, hence allowing for a robust and informed decision-making process under uncertainty. The SA value as a support tool for model-based inference is acknowledged; however, its potential is not fully realized yet within the power system community. This is due to an improper use of long-established SA practices, which sometimes prevent an in-depth model sensitivity investigation, as well as to partial communication between the SA community and the final users, ultimately hindering non-specialists’ awareness of the existence of effective strategies to tackle their own research questions. This paper aims at bridging the gap between SA and power systems via a threefold contribution: (i) a bibliometric study of the state-of-the-art SA to identify common practices in the power system modeling community; (ii) a getting started overview of the most widespread SA methods to support the SA user in the selection of the fittest SA method for a given power system application; (iii) a user-oriented general workflow to illustrate the implementation of SA best practices via a simple technical example.

Ionic liquids (ILs) are highly effective for capturing carbon dioxide (CO 2 ). The prediction of CO 2 solubility in ILs is crucial for optimizing CO 2 capture processes. This study investigates the use of deep learning models for CO 2 solubility prediction in ILs with a comprehensive dataset of 10,116 CO 2 solubility data in 164 kinds of ILs under different temperature and pressure conditions. Deep neural network models, including Artificial Neural Network (ANN) and Long Short-Term Memory (LSTM), were developed to predict CO 2 solubility in ILs. The ANN and LSTM models demonstrated robust test accuracy in predicting CO 2 solubility, with coefficient of determination (R 2 ) values of 0.986 and 0.985, respectively. Both model's computational efficiency and cost were investigated, and the ANN model achieved reliable accuracy with a significantly lower computational time (approximately 30 times faster) than the LSTM model. A global sensitivity analysis (GSA) was performed to assess the influence of process parameters and associated functional groups on CO 2 solubility. The sensitivity analysis results provided insights into the relative importance of input attributes on output variables (CO 2 solubility) in ILs. The findings highlight the significant potential of deep learning models for streamlining the screening process of ILs for CO 2 capture applications.

We rely on a global sensitivity analysis (GSA) approach to identify the dominant physical and biogeochemical controls on dissolved oxygen (DO) dynamics in riparian aquifers. The study is motivated by the observation that availability of DO is key to regulating redox conditions and associated processes in the subsurface. Yet, the complexity of coupled flow and transport models, combined with model input uncertainty challenges our ability to fully characterize system behavior. To address this issue, we integrate Bayesian network‐based and variance‐based methods into a comprehensive GSA framework, enabling a robust evaluation of parameter and process sensitivities. To overcome the high computational demand of GSA for complex numerical models, we develop surrogate models using deep learning approaches (i.e., multi‐layer perceptrons and convolutional neural networks). Application of this framework to a high‐resolution model of riparian DO transport reveals that river stage dynamics (i.e., period and amplitude of water level fluctuations) are primary drivers of DO supply to the aquifer system. Hydraulic conductivity, riverine DO concentration, and the maximum DO reaction rate exhibit important but localized effects, influencing different transport pathways including river water infiltration, entrapped air dissolution, and diffusion through the unsaturated zone. In contrast, parameters such as porosity, longitudinal dispersion, and van Genuchten soil parameters exhibit negligible influence. These findings underscore the value of combining deep learning and GSA to efficiently evaluate complex environmental systems and to guide model simplification and diagnosis.

Global sensitivity analysis (GSA) enhances our understanding of computational models and simplifies model parameter estimation. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a variance‐based GSA framework. The advantage of VISCOUS is that it can use existing model input‐output data (e.g., water model parameters‐responses) to estimate the first‐ and total‐order Sobol’ sensitivity indices. This study improves VISCOUS by refining its handling of marginal densities of the Gaussian mixture copula model (GMCM). We then evaluate VISCOUS using three types of generic functions relevant to water system models. We observe that its performance depends on function dimension, input‐output data size, and non‐identifiability. Function dimension refers to the number of uncertain input factors analyzed in GSA, and non‐identifiability refers to the inability to estimate GMCM parameters. VISCOUS proves powerful in estimating first‐order sensitivity with a small amount of input‐output data (e.g., 200 in this study), regardless of function dimension. It always ranks input factors correctly in both first‐ and total‐order terms. For estimating total‐order sensitivity, it is recommended to use VISCOUS when the function dimension is not very high (e.g., less than 20) due to the challenge of producing sufficient input‐output data for accurate GMCM inferences (e.g., more than 10,000 data). In cases where all input factors are equally important (a rarity in practice), VISCOUS faces non‐identifiability issues that impact its performance. We provide a didactic example and an open‐source Python code, pyVISCOUS, for broader user adoption. Plain Language Summary Global sensitivity analysis is a method used to better understand and estimate parameters in computational models. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a framework for this purpose. It estimates the sensitivity of model outcomes to different uncertain model input factors by using the existing input and output data (e.g., water model parameters and responses). This study improved VISCOUS and tested it with various functions. We found that its performance depends on the number of input factors, the amount of input and output data available, and our ability to determine VISCOUS's parameters. VISCOUS is good at estimating the importance of individual input factors, even with limited data (e.g., 200) and numerous input factors. It always correctly ranks input factor importance, whether individually or collectively. When estimating the importance of input factors together, VISCOUS is recommended when the number of input factors is not very high (e.g., <20), as it is challenging to generate enough input and output data for estimating VISCOUS's parameters. When all input factors hold equal importance (though rare in practice), VISCOUS's performance is impacted due to the difficulty of estimating VISCOUS's parameters. To help people use VISCOUS, we provide an example and an open‐source Python code, pyVISCOUS. Key Points We improve the VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) global sensitivity analysis framework in its handling of marginal densities of the Gaussian mixture copula model We evaluate VISCOUS and demonstrate how its performance is affected by function dimension, input‐output size, and non‐identifiability We provide a didactic example and an open‐source Python code called pyVISCOUS to make VISCOUS easier to understand and apply

Cardiac contraction is the result of integrated cellular, tissue and organ function. Biophysical in silico cardiac models offer a systematic approach for studying these multi-scale interactions. The computational cost of such models is high, due to their multi-parametric and nonlinear nature. This has so far made it difficult to perform model fitting and prevented global sensitivity analysis (GSA) studies. We propose a machine learning approach based on Gaussian process emulation of model simulations using probabilistic surrogate models, which enables model parameter inference via a Bayesian history matching (HM) technique and GSA on whole-organ mechanics. This framework is applied to model healthy and aortic-banded hypertensive rats, a commonly used animal model of heart failure disease. The obtained probabilistic surrogate models accurately predicted the left ventricular pump function ( R 2  = 0.92 for ejection fraction). The HM technique allowed us to fit both the control and diseased virtual bi-ventricular rat heart models to magnetic resonance imaging and literature data, with model outputs from the constrained parameter space falling within 2 SD of the respective experimental values. The GSA identified Troponin C and cross-bridge kinetics as key parameters in determining both systolic and diastolic ventricular function. This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.