Metamodeling Techniques Research Articles

Incorporating Model Uncertainty into Policy Analysis Frameworks: A Bayesian Averaging Approach Combining Computable General Equilibrium (CGE) Model with Metamodelling Techniques

Future sustainable economic development depends heavily on public policy at regional, national, and global levels. Therefore, it is essential to conduct a thorough policy analysis that ensures consistent and effective policy guidance. However, a major challenge in traditional policy analysis is the uncertainty inherent in the models used. Both policymakers and analysts face fundamental uncertainty regarding which model accurately represents the natural, economic, or social phenomena being analyzed. In this paper, we present a comprehensive framework that explicitly incorporates model uncertainty into the policy decision-making process. Addressing this uncertainty typically requires significant computational resources. We utilize metamodeling techniques to reduce computational demands. We illustrate the impact of various metamodel types by applying a simplified model to the CAADP policy in Nigeria. Our findings highlight that neglecting model uncertainty can lead to inefficient policy decisions and substantial waste of public funds.Copyright© 2024 The Author(s). This article is distributed under the terms of the license CC-BY 4.0., which permits any further distribution in any medium, provided the original work is properly cited.

Production Optimization of Premium Food Can with Distortion Printing under Waving Requirement

This research aims to propose a novel approach for evaluating and minimizing scraps in an industrial production of premium food cans with distortion printing. Beyond conventional formability criteria, a waving requirement is introduced to ensure aesthetic quality of the printed graphics. The research focuses on real production conditions, specifically involving double-cold-reduced (DR) low-carbon steel sheets and chromium-coated tin-free steel with a thickness of 0.16 mm. The sheets are laminated on both sides with a plastic film prior to undergoing distortion printing on the exterior. Subsequently, a blank is subjected to a drawing-redrawing process to form a food can. To address challenges associated with characterizing these thin sheets, a material parameter identification method is proposed and demonstrated. The thickness profile and flange length are identified as key criteria for this identification process. Measurements of thickness distribution and flange length are obtained using digital image correlation (DIC) and microscopy techniques. Within the manufacturing system, uncertainties related to material properties and forming processes can result in scraps or defects. To analyze these processes, finite element analysis (FEA) is employed and validated through experiments. For the evaluation of scrap rates, uncertainty propagation is conducted using a metamodeling technique, specifically employing radial basis function (RBF) neural networks. The study concludes by offering process optimization recommendations aimed at reducing the scrap rate.

Reflexive Event-B: Semantics and Correctness the EB4EB Framework

The Event-B method enables correct by construction modeling of systems. It relies on set theory and first-order logic, to describe a series of refined system models expressed as a set of events modifying state variables. Invariants and theorems are introduced to express system properties submitted to the proof system associated with Event-B. While Event-B has proven its efficiency for the proof of this type of property, it does not offer powerful means allowing the explicit description of properties other than safety and specific forms of reachability. Checking other properties such as deadlock-freeness, liveness, or event scheduling requires ad hoc modeling techniques and external tools such as model checkers or other proof systems. This article presents <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EB4EB</i> , a new modeling framework offering the capability to introduce formally defined Event-B extensions, in particular new proof obligations corresponding to new properties. It is based on metamodeling techniques. It includes a theory (a metatheory) modeling Event-B and offers means for explicit manipulation of Event-B features and an extension mechanism to explicitly formalize and prove other properties. This reflexive framework relies on a trace-based semantics of Event-B and introduces a set of Event-B theories defining data types, operators, well-defined conditions, theorems, and proof rules to define Event-B constructs and their semantics. Deep and shallow instantiation mechanisms are set up to instantiate the obtained metatheory. The EB4EB framework and its instantiation mechanisms are developed in Event-B using the Rodin platform ensuring correctness and internal consistency of the defined theories. Lamport's clock example, instantiating EB4EB in both shallow and deep mechanisms, is used to evaluate the proposed approach.

Data-assisted training of a physics-informed neural network to predict the separated Reynolds-averaged turbulent flow field around an airfoil under variable angles of attack

Physics-informed neural networks are a promising method to yield surrogate models of flow fields. We present a metamodeling technique for variable geometries based on physics-informed neural networks. The method was applied to the DU99W350 airfoil at a Reynolds number of 1×105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\ imes 10^{5}$$\\end{document}. Using our technique, the angle of attack was introduced as an additional input parameter of the network and the model was trained to predict the Reynolds-averaged velocity and pressure fields around the airfoil for arbitrary angles of attack between 10.0 and 17.5∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}. Furthermore, we present an effective method to generate the training points for the parameterized geometry. The model was trained with data from simulations for a limited set of angles of attack. Additionally, satisfaction of the a priori known boundary conditions as well as the Reynolds-averaged Navier–Stokes equations was attained. A sensitivity analysis concerning the Reynolds number, the amount and distribution of training data, and the turbulence model was conducted showing the superiority of the pseudo-Reynolds stress method and the demand for labeled training data in the domain. The trained network was capable of predicting the flow separation progressing with angle of attack on the suction surface and exhibited excellent agreement with numerically simulated results, even in the proximity of the wall for interpolations as well as extrapolations from the labeled data set. Our study demonstrates that physics-informed neural networks can be used to obtain accurate flow field surrogate models of variable geometries.

Neuro-Linguistic Programming Meta-Model Techniques in Nadiem's Makarim Speeches and Its Benefits on the Educational Communication

Neuro-Linguistic Programming Meta-Model Techniques in Nadiem's Makarim Speeches and Its Benefits on the Educational Communication

A novel kriging-improved high-dimensional model representation metamodelling technique for approximating high-dimensional problems

Aiming to address the issue of the ‘curse of dimensionality’ encountered in approximating high-dimensional problems using surrogate-based methods, high-dimensional model representation (HDMR), decomposing the high-dimensional problem into summands of different-order component functions, has been widely studied. To reduce the computational demands of the current HDMR metamodelling techniques, an improved high-dimensional model representation framework (iHDMR) is presented, taking full advantage of the relationships between the first-order and second-order component functions in the Cut-HDMR theory. then, a novel metamodelling technique, termed kriging (KRG)-iHDMR, is implemented by integrating the kriging technique and the suggested surface-axes alternating sampling strategy into the iHDMR framework. The accuracy and efficiency of KRG-iHDMR are demonstrated by various numerical and engineering examples with different dimensions. Finally, an optimization problem of the multi-stage solid launch vehicle propulsion system is introduced to verify the engineering feasibility of the KRG-iHDMR metamodelling technique.

Estimation of groundwater age distributions from hydrochemistry: comparison of two metamodelling algorithms in the Heretaunga Plains aquifer system, New Zealand

Abstract. Groundwater age or residence time is important for identifying flow and contaminant pathways through groundwater systems. Typically, groundwater age and age distributions are inferred via lumped parameter models based on measured age tracer concentrations. However, due to cost and time constraints, age tracers are usually only sampled at a small percentage of the wells in a catchment. This paper describes and compares two methods to increase the number of groundwater age data points and assist with validating age distributions inferred from lumped parameter models. Two machine learning techniques with different strengths were applied to develop two independent metamodels that each aim to establish relationships between the hydrochemical parameters and the modelled groundwater age distributions in one test catchment. Ensemble medians from the best model realisations per age distribution percentile were used for comparison with the results from traditional lumped parameter models based on age tracers. Results show that both metamodelling techniques predict age distributions from hydrochemistry with good correspondence to traditional lumped parameter model (LPM)-derived age distributions. Therefore, these techniques can be used to assist with the interpretation of lumped parameter models where age tracers have been sampled, and they can also be applied to predict groundwater age distributions for wells in a similar hydrogeological regime that have hydrochemistry data available but no age tracer data.

Metamodelling of a two-population spiking neural network.

In computational neuroscience, hypotheses are often formulated as bottom-up mechanistic models of the systems in question, consisting of differential equations that can be numerically integrated forward in time. Candidate models can then be validated by comparison against experimental data. The model outputs of neural network models depend on both neuron parameters, connectivity parameters and other model inputs. Successful model fitting requires sufficient exploration of the model parameter space, which can be computationally demanding. Additionally, identifying degeneracy in the parameters, i.e. different combinations of parameter values that produce similar outputs, is of interest, as they define the subset of parameter values consistent with the data. In this computational study, we apply metamodels to a two-population recurrent spiking network of point-neurons, the so-called Brunel network. Metamodels are data-driven approximations to more complex models with more desirable computational properties, which can be run considerably faster than the original model. Specifically, we apply and compare two different metamodelling techniques, masked autoregressive flows (MAF) and deep Gaussian process regression (DGPR), to estimate the power spectra of two different signals; the population spiking activities and the local field potential. We find that the metamodels are able to accurately model the power spectra in the asynchronous irregular regime, and that the DGPR metamodel provides a more accurate representation of the simulator compared to the MAF metamodel. Using the metamodels, we estimate the posterior probability distributions over parameters given observed simulator outputs separately for both LFP and population spiking activities. We find that these distributions correctly identify parameter combinations that give similar model outputs, and that some parameters are significantly more constrained by observing the LFP than by observing the population spiking activities.

A review on the applicability of machine learning techniques to the metamodeling of energy systems

The use of physics-based models for the development and optimization of energy systems is popular due to their versatility. However, their inherent complexity often makes these simulations computationally prohibitive, despite the current computational power available nowadays. This problem is aggravated when considering renewable energy systems, which are subjected to intermittent weather conditions and must be operated in connection with a grid of variable demand. In that sense, the use of metamodels has shown immense potential in the simulation, analysis, and optimization of energy systems. Therefore, this review presents a comprehensive analysis of the extensive application of metamodeling techniques in energy systems. After conducting a careful search using the Scopus database while targeting a well-defined group of keywords, 474 articles published from 2013 to 2023 were obtained in the present literature review. With a rigorous filtering and screening process, the first pool of articles was reduced to 126. The resulting articles were then separated in two main groups, reviews and research articles. Each of these groups was further organized in terms of the energy system studied, as well as the applicability, machine learning technique and error indicator. The results indicate a steady and significant growth in the number of publications associated with energy systems and different types of metamodeling techniques. The reasons are arguably twofold, reduction of computational time provided by the metamodels and their good accuracy. Nevertheless, and as reported by other studies, the review also identified the need to develop a standardized method for evaluating the error analysis of these models and a comparison between their actual efficiency, which includes accuracy and time. Furthermore, no clear relation was found between specific types of metamodels and specific energy systems.

Gradient enhanced gaussian process regression for constitutive modelling in finite strain hyperelasticity

This paper introduces a metamodelling technique that leverages gradient-enhanced Gaussian process regression (also known as gradient-enhanced Kriging), effectively emulating the response of diverse hyperelastic strain energy densities. The approach adopted incorporates principal invariants as inputs for the surrogate of the strain energy density. This integration enables the surrogate to inherently enforce fundamental physical constraints, such as material frame indifference and material symmetry, right from the outset. The proposed approach provides accurate interpolation for energy and the first Piola–Kirchhoff stress tensor (e.g. first order derivatives with respect to inputs). The paper presents three notable innovations. Firstly, it introduces the utilisation of Gradient-Enhanced Kriging to approximate a diverse range of phenomenological models, encompassing numerous isotropic hyperelastic strain energies and a transversely isotropic potential. Secondly, this study marks the inaugural application of this technique for approximating the effective response of composite materials. This includes rank-one laminates, for which analytical solutions are feasible. However, it also encompasses more complex composite materials characterised by a Representative Volume Element (RVE) comprising an elastomeric matrix with a centred spherical inclusion. This extension opens the door for future application of this technique to various RVE types, facilitating efficient three-dimensional computational analyses at the macro-scale of such composite materials, significantly reducing computational time compared to FEM2. The third innovation, facilitated by the integration of these surrogate models into a 3D Finite Element computational framework, lies in the assessment of these models scenarios encompassing intricate cases of extreme twisting and more importantly, buckling instabilities in thin-walled structures, thereby highlighting both the practical applicability and robustness of the proposed approach.

Optomechanical integrated performance analysis and optimization of a greenhouse gas absorption spectrometer

Design of a space-borne opomechanical system with high spatial resolution, spectral resolution and quality imagery demands a tightly integrated performance optimization method to expand the design space and improve the optical performance of the system. In this paper, a Kriging-based method is proposed for optomechanical integrated performance optimization of a greenhouse gas absorption spectrometer (GGAS). The proposed method combines the thermal-structural-optical (TSO) integrated analysis method and the Kriging meta-modeling technique, in which the latter one is used to replace the former analysis process and approximates the I/O functions implied in the underlying TSO simulation model. Structural deformation characteristics and optical performance of GGAS are evaluated firstly. Then, optomechanical structural optimization of GGAS is carried out to achieve lightweight of three sub-benches. Results show that the proposed method is able to reduce the weight of three sub-benches by 11.85 % compared to the common opomechanical design method while satisfying almost the same constraints.

Using Modeling and Metamodels for Reliability Study in Non-Destructive Evaluation

As in any other measurement process, NDE is subject to variability whose impact can be assessed to guarantee a given level of performance. Once NDE prevents catastrophic failures, deaths and environmental damage, identifying uncertainties and variability in NDE help to design more reliable inspections, therefore is a process that saves lives. This is the goal of a reliability study. Statistical indicators such as Probability of Detection (POD) curves give insights to allow building of mechanical designs with enough « secure margin » for structural integrity and to also define appropriate maintenance &amp; inspection cycles. Simulation is very useful to support performance or reliability demonstrations that require a lot of data (such as POD studies and qualification campaigns), and where simulation can help by reducing the number of necessary mock-ups and experimental trials. In addition to physical models, the NDE simulation software CIVA now offers meta-modelling techniques. Built from an initial set of physical simulations, such surrogate models give the user the possibility to generate a massive amount of data while combining and exploring multi parametric variations. This is particularly efficient in the context of reliability studies, when you have to find the best settings, track the worst-case scenario or build POD curves. This paper illustrates the use of this meta-modelling approach for the reliability study of a longitudinal weld AUT inspection. Real pipe mill inspection data are provided and compared to modelling and meta-modelling results.

Role of the front wing/wheel setting-up on the optimal cornering performances of a Formula 1 car

We propose a hybrid approach based on meta-modelling techniques and machine-learning algorithms to determine the best car configuration for each circuit. By a specific interpolation model, we obtain an accurate estimation of the car’s speed as a function of the front wing configuration and the bend curvature. Some high-fidelity fluid dynamic simulations train the model and extend it to the entire design space. These data are then used as input for a simplified car dynamics model, providing an accurate estimate of the ideal lap time. Comparison with actual telemetry data confirms that the resulting tool is reliable, fast and easy to use.

Coastal Flood at Gâvres (Brittany, France): A Simulated Dataset to Support Risk Management and Metamodels Development

Given recent scientific advances, coastal flooding events can be modelled even in complex environments. However, such models are computationally expensive, preventing their use for forecasting. At the same time, metamodelling techniques have been explored for coastal hydrodynamics, showing promising results. Developing such techniques for predicting coastal flood information (e.g., inland water depths) requires large enough learning datasets providing such inland information. However, detailed inland coastal flood observations are scarce and—when available—only correspond to a limited number of events. This paper aims at demonstrating how we can fill this gap by introducing a publicly available dataset, presenting its setup, and providing examples of use and recommendations. It has been built for the site of Gâvres (France), relying on the joint use of spectral wave (WW3) and non-hydrostatic wave-flow (SWASH) models, accounting for wave overtopping. It compiles 250 scenarios (defined by time-varying forcing conditions; including real and stochastically generated events) and the resulting maximal flooded areas and water depths (on 64,618 inland points). Its construction required the equivalent of 2 years of simulations on 48 cores. The examples of use of the dataset focus on method developments (metamodelling, forecast), local knowledge, and risk management.

Probabilistic Failure Envelopes of Monopiles in Scoured Seabed Based on a New Nonstationary Random Field Model

Monopiles, which have been most extensively used in the offshore wind industries, are usually subject to threats from local scour. The effects of local scour on the bearing capacity of monopiles have been studied based on deterministic soil properties and local scour dimensions. However, the properties of the seabed soil and the dimensions of the local scour both have uncertainty. In this study, a new nonstationary random field model, which can better simulate the nonstationary characteristics of the seabed clayey soil and result in a safer probabilistic design of foundations, is proposed to characterize the spatial variability of the seabed clayey soil. Then, the effects of the spatial variability of the seabed clayey soil and the uncertainty of the local scour depth on the bearing capacity of monopiles are investigated under both uniaxial loading and vertical-horizontal-moment (VHM) combined loading using the random finite-element method combined with kriging metamodeling technique and Monte Carlo simulation. The undrained shear strength of the seabed clayey soil was simulated with a lognormally distributed nonstationary random field, and the local scour depth was treated as a uniform random variable. The negative correlation between them was also considered. The results show that the factor of safety required for the local scoured seabed decreased from 3.3 to 2.6 as the negative correlation was enhanced, greater than or equal to that [factor of safety (FS)=2.6] for the intact seabed. The procedure of analyzing the design failure envelop of a monopile in spatially variable clayey soil with a local scour proposed in this study can provide a reference for geotechnical engineers.

Integrating fundamental model uncertainty in policy analysis: A Bayesian averaging approach combining CGE-models with metamodeling techniques

Sustainable economic development in the future is driven by public policy on regional, national and global levels. Therefore a comprehensive policy analysis is needed that provides consistent and effective policy support. However, a general problem facing classical policy analysis is model uncertainty. All actors, those involved in the policy choice and those in the policy analysis, are fundamentally uncertain which of the different models corresponds to the true generative mechanism that represents the natural, economic, or social phenomena on which policy analysis is focused. In this paper, we propose a general framework that explicitly incorporates model uncertainty into the derivation of a policy choice. Incorporating model uncertainty into the analysis is limited by the very high required computational effort. In this regard, we apply metamodeling techniques as a way to reduce computational complexity. We demonstrate the effect of different metamodel types using a reduced model for the case of CAADP in Senegal. Furthermore, we explicitly show that ignoring model uncertainty leads to inefficient policy choices and results in a large waste of public resources.

Probabilistic approach to the stability analysis of caisson foundations under combined loading in spatially variable soil

Caisson foundations are increasingly used in offshore engineering and are usually subjected to combined vertical-horizontal-moment (VHM) loading caused by self-weight, wind, waves, and currents. The bearing capacities of foundations under combined loading are represented by the VHM failure envelopes. In the literatures, failure envelopes for caisson foundations were usually established using a deterministic model of soil properties, ignoring the actual uncertainty and spatial variability of marine soil. The present study focuses on the investigation of the bearing capacities for caissons in spatially variable undrained soil under both uniaxial loading and VHM combined loading. Random finite element method combined with Kriging metamodeling technique and Monte Carlo simulation was applied to evaluate the uniaxial bearing capacities and to define the probabilistic VHM failure envelopes. The soil's undrained shear strength was considered to be increasing with depth, while its coefficient of variation was depth-independent. The effects of the coefficient of variation and scale of fluctuation of undrained shear strength on the uniaxial bearing capacity, on both size and shape of VHM failure envelopes for caisson foundations were discussed. It is shown that spatial variability of soil not only causes a change in the size of the failure envelope but also affects its shape when compared with the deterministic case. Therefore, it is necessary to consider the spatial variability of soil when designing caisson foundations and the present results provide some guidance for the design.

Queueing inspired feature engineering to improve and simplify patient flow simulation metamodels

ABSTRACT We explore the interplay between domain-informed feature engineering, model performance, and model interpretability. This is a hybrid modelling and simulation study that merges the application of discrete-event simulation with alternative metamodelling techniques for modelling patient flow in health care. We consider two cases: a tandem queueing system of obstetric hospital units and a transient analysis of an outpatient clinic in which a finite number of scheduled patients arrive for care. We use several metamodels including various types of linear models, random forests, and neural networks. We evaluate the performance improvement of metamodel estimation when empowered with supplementary queueing theory knowledge. We consider three knowledge levels: no knowledge (no queueing-inspired features), basic (simple queueing features), and advanced (sophisticated queueing approximations). Our results show that queueing-related inputs improve the accuracy for the metamodels, independent of the model type. Moreover, queueing-related inputs improve model explainability and can lead to more parsimonious models. This has positive practical implications for implementing these types of models in actual health-care analytic projects.

Real-Time Hybrid Simulation Using Nonlinear Autoregressive with Exogenous Input Model through Data-Driven Arbitrary Polynomial Chaos Surrogate

The current practice of real-time hybrid simulation (RTHS) often requires specialized finite element programs for computational modeling of the analytical substructures. Considering the limited nonlinear modeling capacity or the increasing computation cost for complex modeling, surrogate models of the analytical substructure provide novel alternatives for RTHS to avoid finite element analysis with fast computation. This study explores the use of arbitrary polynomial chaos expansion (APC) and nonlinear autoregressive with exogenous input (NARX) model to emulate the dynamic behavior of analytical substructures in RTHS. The NARX model training can be conducted numerically in an off-line mode using existing general purpose finite element analysis software, and its implementation presents minimum computational demands on the RTHS equipment. RTHS of a single-degree-of-freedom structure with a self-centering viscous damper is conducted as proof of concept to experimentally demonstrate the effectiveness and superiority of the proposed APC-NARX-based approach. The APC is further compared with other metamodeling techniques including polynomial chaos expansion (PCE) and Kriging to surrogate NARX model coefficients to account for ground motion uncertainties in RTHS. It is demonstrated that APC-NARX modeling with optimal order enables better accuracy of RTHS results than those of Kriging- and PCE-NARX.

Lead-Free Piezoelectric Acceleration Sensor Built Using a (K,Na)NbO3 Bulk Ceramic Modified by Bi-Based Perovskites

Piezoelectric accelerometers using a lead-free (K,Na)NbO3 (KNN) piezoceramic modified by a mixture of two Bi-based perovskites, Bi(Na,K,Li)ZrO3 (BNKLZ) and BiScO3 (BS), were designed, fabricated and characterized. Ring-shaped ceramics were prepared using a conventional solid-state reaction method for integration into a compression-mode accelerometer. A beneficial rhombohedral-tetragonal (R-T) phase boundary structure, especially enriched with T phase, was produced by modifying intrinsic phase transition temperatures, yielding a large piezoelectric charge coefficient d33 (310 pC/N) and a high Curie temperature Tc (331 °C). Using finite element analyses with metamodeling techniques, four optimum accelerometer designs were obtained with high magnitudes of charge sensitivity Sq and resonant frequency fr, as evidenced by two key performance indicators having a trade-off relation. Finally, accelerometer sensor prototypes based on the proposed designs were fabricated using the KNN-BNKLZ-BS ceramic rings, which exhibited high levels of Sq (55.1 to 223.8 pC/g) and mounted fr (14.1 to 28.4 kHz). Perfect charge-to-acceleration linearity as well as broad flat frequency ranges were achieved with excellent reliability. These outstanding sensing performances confirm the potential application of the modified-KNN ceramic in piezoelectric sensors.