Sampling High Dimensional Model Representation Research Articles

Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for representing multidimensional functions with machine-learned lower-dimensional terms allowing insight with a general method

We present an implementation for the RS-HDMR-GPR (Random Sampling High Dimensional Model Representation Gaussian Process Regression) method. The method builds representations of multivariate functions with lower-dimensional terms, either as an expansion over orders of coupling or using terms of only a given dimensionality. This facilitates, in particular, recovering functional dependence from sparse data. The method also allows for imputation of missing values of the variables and for a significant pruning of the useful number of HDMR terms. It can also be used for estimating relative importance of different combinations of input variables, thereby adding an element of insight to a general machine learning method, in a way that can be viewed as extending the automatic relevance determination approach. The capabilities of the method and of the associated Python software tool are demonstrated on test cases involving synthetic analytic functions, the potential energy surface of the water molecule, kinetic energy densities of materials (crystalline magnesium, aluminum, and silicon), and financial market data.

Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for Multivariate Function Representation: Application to Molecular Potential Energy Surfaces.

We present an approach combining a representation of a multivariate function using subdimensional functions with machine learning based representation of component functions: Random sampling high dimensional model representation Gaussian process regression (RS-HDMR-GPR). The use of Gaussian process regressions to represent component functions allows nonparametric (unbiased) representation and the possibility to work only with functions of desired dimensionality, obviating the need to build an expansion over orders of coupling. All component functions are determined from a single set of samples. The method is tested by fitting six- and 15-dimensional potential energy surfaces (PES) of polyatomic molecules as well as by computing vibrational spectra for a four-atomic molecule.

An Innovative Methodology for Online Surrogate-Based Model Updating of Historic Buildings Using Monitoring Data

ABSTRACT Structural Health Monitoring (SHM) based on Automated Operational Modal Analysis (A-OMA) has gained increasing importance in the conservation of heritage structures over recent decades. In this context, finite element model updating techniques using modal data constitute a commonly used approach for damage identification. Nevertheless, the large number of simulations usually involved in the associated minimization problem hinders the application to real-time condition assessment. This is especially critical for historic buildings, where the modelling of complex geometries involves large computational burdens. Alternatively, surrogate models offer an efficient solution to replace computationally demanding numerical models and so perform continuous model updating. In this light, this paper presents a surrogate-based model updating approach for online assessment of historic buildings and its application to a medieval masonry tower, the Sciri Tower in Perugia (Italy). Using modal properties identified by A-OMA, the proposed approach allows the continuous fitting of certain damage-sensitive parameters of the structure. To do so, three different surrogate models are considered, including the quadratic response surface method, Kriging, and Random Sampling High-Dimensional Model Representation, and their effectiveness is compared from an SHM perspective. The reported results demonstrate the suitability of the proposed methodology for tracking the temperature-dependent intrinsic properties of the tower.

A global sensitivity analysis-assisted sequential optimization tool for plant-fin heat sink design

Purpose This study aims to suggest and develops a global sensitivity analysis-assisted multi-level sequential optimization method for the heat transfer problem. Design/methodology/approach Compared with other surrogate-assisted optimization methods, the distinctive characteristic of the suggested method is to decompose the original problem into several layers according to the global sensitivity index. The optimization starts with the several most important design variables by the support vector regression-based efficient global optimization method. Then, when the optimization process progresses, the filtered design variables should be involved in optimization one by one or the setting value. Therefore, in each layer, the design space should be reduced according to the previous optimization result. To improve the accuracy of the global sensitivity index, a novel global sensitivity analysis method based on the variance-based method incorporating a random sampling high-dimensional model representation is introduced. Findings The advantage of this method lies in its capability to solve complicated problems with a limited number of sample points. Moreover, to enhance the reliability of optimum, the support vector regression-based global efficient optimization is used to optimize in each layer. Practical implications The developed optimization tool is built by MATLAB and can be integrated by commercial software, such as ABAQUS and COMSOL. Lastly, this tool is integrated with COMSOL and applied to the plant-fin heat sink design. Compared with the initial temperature, the temperature after design is over 49°. Moreover, the relationships among all design variables are also disclosed clearly. Originality/value The D-MORPH-HDMR is integrated to obtain the coupling relativities among the design variables efficiently. The suggested method can be decomposed into multiplier layers according to the GSI. The SVR-EGO is used to optimize the sub-problem because of its robustness of modeling.

Investigation of the effect of correlated uncertain rate parameters via the calculation of global and local sensitivity indices

Applications of global uncertainty methods for models with correlated parameters are essential to investigate chemical kinetics models. A global sensitivity analysis method is presented that is able to handle correlated parameter sets. It is based on the coupling of the Rosenblatt transformation with an optimized Random Sampling High Dimensional Model Representation method. The accuracy of the computational method was tested on a series of examples where the analytical solution was available. The capabilities of the method were also investigated by exploring the effect of the uncertainty of rate parameters of a syngas–air combustion mechanism on the calculated ignition delay times. Most of the parameters have large correlated sensitivity indices and the correlation between the parameters has a high influence on the results. It was demonstrated that the values of the calculated total correlated and final marginal sensitivity indices are independent of the order of the decorrelation steps. The final marginal sensitivity indices are meaningful for the investigation of the chemical significance of the reaction steps. The parameters belonging to five elementary reactions only, have significant final marginal sensitivity indices. Local sensitivity indices for correlated parameters were defined which are the linear equivalents of the global ones. The results of the global sensitivity analysis were compared with the corresponding results of local sensitivity analysis for the case of the syngas–air combustion system. The same set of reactions was indicated to be important by both approaches.

Global sensitivity analysis of a mathematical model of acute inflammation identifies nonlinear dependence of cumulative tissue damage on host interleukin-6 responses

The precise inflammatory role of the cytokine interleukin (IL)-6 and its utility as a biomarker or therapeutic target have been the source of much debate, presumably due to the complex pro- and anti-inflammatory effects of this cytokine. We previously developed a nonlinear ordinary differential equation (ODE) model to explain the dynamics of endotoxin (lipopolysaccharide; LPS)-induced acute inflammation and associated whole-animal damage/dysfunction (a proxy for the health of the organism), along with the inflammatory mediators tumor necrosis factor (TNF)-α, IL-6, IL-10, and nitric oxide (NO). The model was partially calibrated using data from endotoxemic C57Bl/6 mice. Herein, we investigated the sensitivity of the area under the damage curve (AUCD) to the 51 rate parameters of the ODE model for different levels of simulated LPS challenges using a global sensitivity approach called Random Sampling High Dimensional Model Representation (RS-HDMR). We explored sufficient parametric Monte Carlo samples to generate the variance-based Sobol’ global sensitivity indices, and found that inflammatory damage was highly sensitive to the parameters affecting the activity of IL-6 during the different stages of acute inflammation. The AUCIL6 showed a bimodal distribution, with the lower peak representing healthy response and the higher peak representing sustained inflammation. Damage was minimal at low AUCIL6, giving rise to a healthy response. In contrast, intermediate levels of AUCIL6 resulted in high damage, and this was due to the insufficiency of damage recovery driven by anti-inflammatory responses from IL-10 and the activation of positive feedback sustained by IL-6. At high AUCIL6, damage recovery was interestingly restored in some population of simulated animals due to the NO-mediated anti-inflammatory responses. These observations suggest that the host׳s health status during acute inflammation depends in a nonlinear fashion on the magnitude of the inflammatory stimulus, on the host׳s propensity to produce IL-6, and on NO-mediated downstream responses.

Uncertainty propagation in the derivation of phenomenological rate coefficients from theory: A case study of n-propyl radical oxidation

Global uncertainty and sensitivity analysis is used to study the propagation of uncertainties in fundamental theoretical parameters through to uncertainties in the predicted temperature and pressure dependent phenomenological rate coefficients. Predictions are obtained from ab initio transition state theory based master equation calculations. The fundamental parameters for these rate predictions include barrier heights, well depths, vibrational frequencies, collision frequency, and energy transfer parameters. A random sampling high-dimensional model representation (HDMR) approach is used to perform the global sensitivity analysis. This approach determines the predicted distributions of the phenomenological rate coefficients based on a quasi-random sample of the fundamental parameters within their uncertainty range. Sensitivity analysis then identifies the main parameters which contribute to variance in the predicted distributions. Here the approach is applied to a study of the oxidation of the propyl radical, employing the parameters derived in our recent theoretical study. We find rates at 3σ variances that typically differ from the most frequent values by factors of 4–6, with the uncertainties decreasing with increasing temperature. For the well skipping reactions there are more parameters that contribute significantly to the variance, the second-order sensitivities are greater, and the uncertainties increased with increasing pressure. For the other reactions, the uncertainties tend to decrease with increasing pressure.

Optimizing Genetic Circuits by Global Sensitivity Analysis

Artificial genetic circuits are becoming important tools for controlling cellular behavior and studying molecular biosystems. To genetically optimize the properties of complex circuits in a practically feasible fashion, it is necessary to identify the best genes and/or their regulatory components as mutation targets to avoid the mutation experiments being wasted on ineffective regions, but this goal is generally not achievable by current methods. The Random Sampling—High Dimensional Model Representation (RS-HDMR) algorithm is employed in this work as a global sensitivity analysis technique to estimate the sensitivities of the circuit properties with respect to the circuit model parameters, such as rate constants, without knowing the precise parameter values. The sensitivity information can then guide the selection of the optimal mutation targets and thereby reduce the laboratory effort. As a proof of principle, the in vivo effects of 16 pairwise mutations on the properties of a genetic inverter were compared against the RS-HDMR predictions, and the algorithm not only showed good consistency with laboratory results but also revealed useful information, such as different optimal mutation targets for optimizing different circuit properties, not available from previous experiments and modeling.

Simulating bioremediation of uranium-contaminated aquifers; uncertainty assessment of model parameters

Bioremediation of trace metals and radionuclides in groundwater may require the manipulation of redox conditions via the injection of a carbon source. For example, after nitrate has been reduced, soluble U(VI) can be reduced simultaneously with other electron acceptors such as Fe(III) or sulfate to U(IV), which may precipitate as a solid (uraninite). To simulate the numerous biogeochemical processes that will occur during the bioremediation of trace-metal-contaminated aquifers, a time-dependent one-dimensional reactive transport model has been developed. The model consists of a set of coupled mass balance equations, accounting for advection, hydrodynamic dispersion, and a kinetic formulation of the biological or chemical transformations affecting an organic substrate, electron acceptors, corresponding reduced species, and trace metal contaminants of interest, uranium in this study. This set of equations is solved numerically, using a finite difference approximation. The redox conditions of the domain are characterized by estimating the pE, based on the concentration of the dominant terminal electron acceptor and its corresponding reduced species. This pE and the concentrations of relevant species are then used by a modified version of MINTEQA2, which calculates the speciation/sorption and precipitation/dissolution of the species of interest under equilibrium conditions. Kinetics of precipitation/dissolution processes are described as being proportional to the difference between the actual and calculated equilibrium concentration. A global uncertainty assessment, determined by Random Sampling High Dimensional Model Representation (RS-HDMR), was performed to attain a phenomenological understanding of the origins of output variability and to suggest input parameter refinements as well as to provide guidance for field experiments to improve the quality of the model predictions. By decomposing the model output variance into its different input contributions, RS-HDMR can identify the model inputs with the most influence on various model outputs, as well as their behavior pattern on the model output. Simulations are performed to illustrate the effect of biostimulation on the fate of uranium in a saturated aquifer, and to identify the key processes that need to be characterized with the highest accuracy prior to designing a uranium bioremediation scheme.