Gaussian Process Metamodeling Research Articles

Uncertainty analysis of curing-induced dimensional variability of composite structures utilizing physics-guided Gaussian process meta-modeling

Composite manufacturing process involves a suite of complex and inter-related procedures that span across multiple physics domains and scales. A variety of uncertainties that inevitably exist may degrade the quality of composites produced. Quantitatively characterizing the effect of uncertainties in such process hence becomes critically important. In this study, we establish a systematic framework for uncertainty analysis of composite manufacturing process. A finite element processing model has been developed to characterize the multi-physics and multi-scale nature of composite manufacturing process, based upon which a Gaussian process (GP) meta-model has been synthesized for efficient uncertainty quantification. By leveraging the well-trained GP meta-model, an importance ranking analysis of uncertainties was then carried out using a series of metrics, i.e., Pearson coefficient, Sobol index and Shapley Additive exPlanations (SHAP). Since the physics-based processing model involves several simplifying assumptions and empirical relations, modeling errors were also considered in the uncertainty analysis. Comprehensive case studies, which aim at elucidating the causes of composite spring-in angles, were conducted to examine the feasibility and validity of this new framework. Specifically, the mean error of GP predictions is smaller than 2%, and the uncertainty importance ranking can be obtained with high confidence in both cases with and without modeling errors.

StormSim-CHRPS: Coastal Hazards Rapid Prediction System

Torres, M.J.; Nadal-Caraballo, N.C.; Ramos-Santiago, E.; Campbell, M.O.; Gonzalez, V.M.; Melby, J.A., and Taflanidis, A.A., 2020. StormSim-CHRPS: Coastal Hazards Rapid Prediction System. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1320-1325. Coconut Creek (Florida), ISSN 0749-0208.Recent advances in high-performance computing and numerical modeling have resulted in the development of high-fidelity storm surge and wave simulation models that produce accurate and detailed representation of physical (hydrodynamic) processes that can support high-accuracy forecasting applications. Unfortunately, the computational demand of these high-fidelity models makes practical application for real-time emergency management and operations challenging. However, metamodeling of storm response has matured to the point of application and has the advantage of extremely fast simulation with only minor degradation of accuracy. The StormSim Coastal Hazards Rapid Prediction System (StormSim-CHRPS) performs rapid prediction of coastal storm hazards, including real-time hurricane-induced flooding and risk assessment. Its enhanced computational efficiency was developed using a machine learning method called Gaussian process metamodeling (GPM). As a result, StormSim-CHRPS predictions preserve the accuracy of the high-fidelity hydrodynamic numerical models archived and distributed through the Coastal Hazards System (CHS). A hurricane parametrization approach employed in coastal hazard studies, known as the joint probability method (JPM), provides the input to the GPM. Possible GPM outputs include a wide range of coastal hazards, including storm surge, wave height, period, and direction, currents, wind, and rainfall. The implementation of GPM allows StormSim-CHRPS to efficiently and accurately predict the response of a hurricane ensemble in a matter of a few seconds and tens of thousands of different hurricane scenarios in a few minutes, within a probabilistic rapid prediction framework, making it an ideal technology for real-time hazard prediction and long-term risk assessment applications.

Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

This paper investigates the construction of a metamodel for coastal flooding early warning at the peninsula of Gâvres, France. The code under study is an hydrodynamic model which receives time-varying maritime conditions as inputs. We concentrate on Gaussian pocess metamodels to emulate the behavior of the code. To model the inputs we make a projection of them onto a space of lower dimension. This setting gives rise to a model selection methodology which we use to calibrate four characteristics of our functional-input metamodel: (i) the family of basis functions to project the inputs; (ii) the projection dimension; (iii) the distance to measure similarity between functional input points; and (iv) the set of functional predictors to keep active. The proposed methodology seeks to optimize these parameters for metamodel predictability, at an affordable computational cost. A comparison to a dimensionality reduction approach based on the projection error of the input functions only showed that the latter may lead to unnecessarily large projection dimensions. We also assessed the adaptability of our methodology to changes in the number of training and validation points. The methodology proved its robustness by finding the optimal solution for most of the instances, while being computationally efficient.

Materials by Design for Stiff and Tough Hairy Nanoparticle Assemblies.

Matrix-free polymer-grafted nanocrystals, called assembled hairy nanoparticles (aHNPs), can significantly enhance the thermomechanical performance of nanocomposites by overcoming nanoparticle dispersion challenges and achieving stronger interfacial interactions through grafted polymer chains. However, effective strategies to improve both the mechanical stiffness and toughness of aHNPs are lacking given the general conflicting nature of these two properties and the large number of molecular parameters involved in the design of aHNPs. Here, we propose a computational framework that combines multiresponse Gaussian process metamodeling and coarse-grained molecular dynamics simulations to establish design strategies for achieving optimal mechanical properties of aHNPs within a parametric space. Taking poly(methyl methacrylate) grafted to high-aspect-ratio cellulose nanocrystals as a model nanocomposite, our multiobjective design optimization framework reveals that the polymer chain length and grafting density are the main influencing factors governing the mechanical properties of aHNPs, in comparison to the nanoparticle size and the polymer-nanoparticle interfacial interactions. In particular, the Pareto frontier, that marks the upper bound of mechanical properties within the design parameter space, can be achieved when the weight percentage of nanoparticles is above around 60% and the grafted chains exceed the critical length scale governing transition into the semidilute brush regime. We show that theoretical scaling relationships derived from the Daoud-Cotton model capture the dependence of the critical length scale on graft density and nanoparticle size. Our established modeling framework provides valuable insights into the mechanical behavior of these hairy nanoparticle assemblies at the molecular level and allows us to establish guidelines for nanocomposite design.

A Bayesian approach for characterization of soft tissue viscoelasticity in acoustic radiation force imaging.

Biomechanical imaging techniques based on acoustic radiation force (ARF) have been developed to characterize the viscoelasticity of soft tissue by measuring the motion excited by ARF non-invasively. The unknown stress distribution in the region of excitation limits an accurate inverse characterization of soft tissue viscoelasticity, and single degree-of-freedom simplified models have been applied to solve the inverse problem approximately. In this study, the ARF-induced creep imaging is employed to estimate the time constant of a Voigt viscoelastic tissue model, and an inverse finite element (FE) characterization procedure based on a Bayesian formulation is presented. The Bayesian approach aims to estimate a reasonable quantification of the probability distributions of soft tissue mechanical properties in the presence of measurement noise and model parameter uncertainty. Gaussian process metamodeling is applied to provide a fast statistical approximation based on a small number of computationally expensive FE model runs. Numerical simulation results demonstrate that the Bayesian approach provides an efficient and practical estimation of the probability distributions of time constant in the ARF-induced creep imaging. In a comparison study with the single degree of freedom models, the Bayesian approach with FE models improves the estimation results even in the presence of large uncertainty levels of the model parameters.

Global sensitivity analysis of large-scale numerical landslide models based on Gaussian-Process meta-modeling

Large-scale landslide prediction is typically based on numerical modeling, with computer codes generally involving a large number of input parameters. Addressing the influence of each of them on the final result and providing a ranking procedure may be useful for risk management purposes. This can be performed by a variance-based global sensitivity analysis. Nevertheless, such an analysis requires a large number of computer code simulations, which appears impracticable for computationally demanding simulations, with computation times ranging from several hours to several days. To overcome this difficulty, we propose a “meta-model”-based strategy consisting in replacing the complex simulator by a “statistical approximation” provided by a Gaussian-process (GP) model. This allows computation of sensitivity measures from a limited number of simulations. For illustrative purposes, the proposed methodology is used to rank in terms of importance the properties of the elastoplastic model describing the complex behavior of the slip surface in the La Frasse landslide (Switzerland). One limitation of the GP-based methodology is that the computation of sensitivity measures is associated with uncertainty as the simulator is approximated using a training sample of small size, i.e., a limited knowledge on the “true” simulator. This source of uncertainty can be taken into account by treating the GP model from a Bayesian perspective. This provides the full posterior probability distribution associated with the sensitivity measures, which can be summarized by a confidence interval to outline the regions where the GP model is “unsure.” We show that this methodology is able to provide useful guidelines for the practical decision-making process and suggest further site investigations.

Gaussian Process Metamodeling in Bayesian Value of Information Analysis: A Case of the Complex Health Economic Model for Breast Cancer Screening

Objectives To determine whether allocation of resources into further research of breast cancer screening is warranted; also, to identify the parameters, for which the information would be most valuable, to prioritize the further research if deemed justifiable. Methods The Bayesian value of information analysis was conducted to calculate the overall expected value of perfect information (EVPI) and the partial EVPI for the six groups of parameters. Computational expense of the partial EVPI calculation was challenged with the use of Multiple Linear Regression and Gaussian Process metamodels to significantly cut down the computing time. Results Of the two metamodeling techniques, the Gaussian Process was proven to perform superiorly and was therefore chosen for the partial EVPI calculation. The results indicate a considerable range in the population EVPI estimates, between €100 and €500 millions at the willingness-to-pay values between €10,000 and €40,000 per quality-adjusted life-year. The partial EVPI for the groups of parameters indicated that future research would be most valuable if directed toward obtaining more precise estimates of the cancer sojourn times. With the use of the Gaussian process metamodels, the computing time was reduced from 44 years to 47 days. Conclusions Although the large values of EVPI suggest collection of further information before choosing the screening policy, it is argued that delaying the decision would result in significantly higher opportunity loss. Therefore, the best option would be to implement the most cost-effective policy given the existing information (screening women aged 40–80 years, at 3-year intervals) and simultaneously conduct observational studies alongside the implemented policy. The decision analytic model could be in this manner periodically updated with additional information as it became available and the most cost-effective policy chosen iteratively.