Surrogate Metamodels Research Articles

Surrogate metamodels from digital image correlation for testing high-performance composite vessels

In this work, a workflow has been developed for the generation of surrogate metamodels to predict and evaluate failure with a confidence above 95 % in initial service conditions of high-performance cylindrical vessels manufactured in composites by Roll Wrapping technology. Currently, there is no specific testing standardization for this type of vessel and to fill this gap probabilistic numerical models were developed, performed by the Finite Element Method, fed with the material characteristics obtained experimentally by 2D digital image correlation from flat specimens. From the initial numerical model, a surrogate metamodel was generated by stochastic approximations. Once the metamodels were obtained by robust engineering, an experimental ring-ring tensile test was developed under service conditions and deformations were measured by high-precision 3D digital image correlation. Parametric and robust tests showed that the results of the metamodel did not show statistically significant differences, with errors in the rupture part of less than 2 % with respect to the results obtained in the test, being proposed as a basis for new test procedures.

An adaptive marine predator algorithm based optimization method for hood lightweight design

Abstract The lightweight design of the hood is crucial for the structural optimization of an entire vehicle. However, traditional high-fidelity-based lightweight methods are time-consuming due to the complex structures of the hood, and the lightweight results heavily rely on engineering experiences. To this end, an improved adaptive marine predator algorithm (AMPA) is proposed to solve this problem. Compared to the original marine predator algorithm (MPA), the proposed AMPA adapts to optimization problems through three enhancements, including chaotic theory-based initialization, a mixed search strategy, and dynamic partitioning of iteration phases. Experimental comparisons of AMPA, MPA, and eight state-of-the-art algorithms are conducted on IEEE CEC2017 benchmark functions. AMPA outperforms the others in both 30- and 50-dimensional experiments. Friedman and Wilcoxon’s sign-rank tests further confirm AMPA’s superiority and statistical significance. An implicit parametric model of the hood is generated, and the critical design variables are determined through global sensitivity analysis to realize hood lightweight. The stacking method is employed to construct a surrogate meta-model of the hood to accelerate the optimization efficiency of the vehicle hood. Utilizing the meta-model and the proposed AMPA, the hood mass is reduced by 7.43% while all six static and dynamic stiffness metrics are enhanced. The effectiveness of the proposed optimization method is validated through finite element analysis.

Microseismic event detection in large heterogeneous velocity models using Bayesian multimodal nested sampling

Abstract In passive seismic and microseismic monitoring, identifying and characterizing events in a strong noisy background is a challenging task. Most of the established methods for geophysical inversion are likely to yield many false event detections. The most advanced of these schemes require thousands of computationally demanding forward elastic-wave propagation simulations. Here we train and use an ensemble of Gaussian process surrogate meta-models, or proxy emulators, to accelerate the generation of accurate template seismograms from random microseismic event locations. In the presence of multiple microseismic events occurring at different spatial locations with arbitrary amplitude and origin time, and in the presence of noise, an inference algorithm needs to navigate an objective function or likelihood landscape of highly complex shape, perhaps with multiple modes and narrow curving degeneracies. This is a challenging computational task even for state-of-the-art Bayesian sampling algorithms. In this paper, we propose a novel method for detecting multiple microseismic events in a strong noise background using Bayesian inference, in particular, the Multimodal Nested Sampling (MultiNest) algorithm. The method not only provides the posterior samples for the 5D spatio-temporal-amplitude inference for the real microseismic events, by inverting the seismic traces in multiple surface receivers, but also computes the Bayesian evidence or the marginal likelihood that permits hypothesis testing for discriminating true vs. false event detection.

Managing uncertainty in data-driven simulation-based optimization

Optimization using data from complex simulations has become an attractive decision-making option, due to ability to embed high-fidelity, non-linear understanding of processes within the search for optimal values. Due to lack of tractable algebraic equations, the link between simulations and optimization is oftentimes a surrogate metamodel. However, several forms of uncertainty exist within the cycle that links simulation data, to metamodels, to optimization. Uncertainty may originate from parameters of the simulation, or the form and fitted parameters of the metamodel. This paper reviews different literatures that are relevant to surrogate-based optimization and proposes different strategies for handling uncertainty, by combining machine learning with stochastic programming, robust optimization, and discrepancy modeling. We show that incorporating uncertainty management within simulation-based optimization leads to more robust solutions, which protect the decision-maker from infeasible solutions. We present the results of our proposed approaches through a case study for direct-air capture through temperature swing adsorption.

A cubature collocation based sparse polynomial chaos expansion for efficient structural reliability analysis

Polynomial chaos expansion (PCE) is widely used to build a surrogate meta-model of the performance function for structural reliability analysis. The number of terms to be determined in PCE grows exponentially with the number of input random variables, which makes the computational effort intractable in practices. Although several sparse PCEs have been developed, a large number of deterministic model evaluations may be still required to achieve a satisfactory accuracy since equal-weighted collocation samples are used. To address such problems, this paper proposes a cubature collocation based sparse PCE for efficient structural reliability analysis. An iterative scheme is actually involved in the proposed method, which automatically selects the significant terms in PCE contributing to the variance of the performance function. The cubature formula not only generates unequal-weighted collocation samples, which has much faster convergent rate, but also provides the target variance of the performance function to terminate the iterative process. In this regard, a weighted regression method is employed in each step to determine the coefficients of PCE. As a consequence, a rather small number of terms in PCE are retained. Since the number of cubature collocation points is relatively small, the construction of a sparse PCE is quite efficient. Several numerical examples are investigated to validate the proposed method for structural reliability analysis. The results show the effectiveness of the proposed method for different reliability problems.

Agent-based model calibration using machine learning surrogates

Efficiently calibrating agent-based models (ABMs) to real data is an open challenge. This paper explicitly tackles parameter space exploration and calibration of ABMs by combining machine-learning and intelligent iterative sampling. The proposed approach “learns” a fast surrogate meta-model using a limited number of ABM evaluations and approximates the nonlinear relationship between ABM inputs (initial conditions and parameters) and outputs. Performance is evaluated on the Brock and Hommes (1998) asset pricing model and the “Islands” endogenous growth model Fagiolo and Dosi (2003). Results demonstrate that machine learning surrogates obtained using the proposed iterative learning procedure provide a quite accurate proxy of the true model and dramatically reduce the computation time necessary for large scale parameter space exploration and calibration.

Enhance crashworthiness of composite structures using gradient honeycomb material

ABSTRACTLightweight cellular materials can effectively improve the crashworthiness of thin-walled structures. To further investigate the potential of honeycomb-filled thin-walled structures, this paper proposed a novel functionally graded honeycomb (FGH) as filler. First, the finite element model of the functionally graded honeycomb-filled tube (FGHT) is established and validated via experimental results. Then, the key factors of FGHT for crashworthiness are identified. The results show that gradient pattern is critical to the crushing response. As for the overall energy absorption capability, we thoroughly examined the effects of gradient exponent n and the thickness range of honeycomb shells. Next, we conducted single and multi-objective optimisation, adopting genetic algorithm (GA) and non-dominated sorting genetic algorithm (NSGA-II), to seek the parameters that deliver overall crashworthiness performance. The Kriging surrogate metamodel was established to formulate specific energy absorption (SEA) and peak crushing force (PCF) in relation to the key parameters. The single objective optimisation revealed that, provided the same PCF, the SEA of FGHT is always higher than uniform honeycomb filled tube (UHFT); the Pareto front obtained from multi-objective optimisation also indicate that FGHT is generally more efficient than UHFT. This paper gives insights on the honeycomb-filled materials to achieve maximum crashworthiness performance.

Agent-Based Model Calibration Using Machine Learning Surrogates

Efficiently calibrating agent-based models (ABMs) to real data is an open challenge. This paper explicitly tackles parameter space exploration and calibration of ABMs by combining machine-learning and intelligent iterative sampling. The proposed approach learns a fast surrogate meta-model using a limited number of ABM evaluations and approximates the nonlinear relationship between ABM inputs (initial conditions and parameters) and outputs. Performance is evaluated on the (Brock and Hommes, 1998) asset pricing model and the Islands endogenous growth model (Fagiolo and Dosi, 2003). Results demonstrate that machine learning surrogates obtained using the proposed iterative learning procedure provide a quite accurate proxy of the true model and dramatically reduce the computation time necessary for large scale parameter space exploration and calibration.

Emulation of Leaf, Canopy and Atmosphere Radiative Transfer Models for Fast Global Sensitivity Analysis

Physically-based radiative transfer models (RTMs) help understand the interactions of radiation with vegetation and atmosphere. However, advanced RTMs can be computationally burdensome, which makes them impractical in many real applications, especially when many state conditions and model couplings need to be studied. To overcome this problem, it is proposed to substitute RTMs through surrogate meta-models also named emulators. Emulators approximate the functioning of RTMs through statistical learning regression methods, and can open many new applications because of their computational efficiency and outstanding accuracy. Emulators allow fast global sensitivity analysis (GSA) studies on advanced, computationally expensive RTMs. As a proof-of-concept, three machine learning regression algorithms (MLRAs) were tested to function as emulators for the leaf RTM PROSPECT-4, the canopy RTM PROSAIL, and the computationally expensive atmospheric RTM MODTRAN5. Selected MLRAs were: kernel ridge regression (KRR), neural networks (NN) and Gaussian processes regression (GPR). For each RTM, 500 simulations were generated for training and validation. The majority of MLRAs were excellently validated to function as emulators with relative errors well below 0.2%. The emulators were then put into a GSA scheme and compared against GSA results as generated by original PROSPECT-4 and PROSAIL runs. NN and GPR emulators delivered identical GSA results, while processing speed compared to the original RTMs doubled for PROSPECT-4 and tripled for PROSAIL. Having the emulator-GSA concept successfully tested, for six MODTRAN5 atmospheric transfer functions (outputs), i.e., direct and diffuse at-surface solar irradiance ( E d i f , E d i r ), direct and diffuse upward transmittance ( T d i r , T d i f ), spherical albedo (S) and path radiance ( L 0 ), the most accurate MLRA’s were subsequently applied as emulator into the GSA scheme. The sensitivity analysis along the 400–2500 nm spectral range took no more than a few minutes on a contemporary computer—in comparison, the same analysis in the original MODTRAN5 would have taken over a month. Key atmospheric drivers were identified, which are on the one hand aerosol optical properties, i.e., aerosol optical thickness (AOT), Angstrom coefficient (AMS) and scattering asymmetry variable (G), mostly driving diffuse atmospheric components, E d i f and T d i f ; and those affected by atmospheric scattering, L 0 and S. On the other hand, as expected, AOT, AMS and columnar water vapor (CWV) in the absorption regions mostly drive E d i r and T d i r atmospheric functions. The presented emulation schemes showed very promising results in replacing costly RTMs, and we think they can contribute to the adoption of machine learning techniques in remote sensing and environmental applications.

Regulatory interactions maintaining self-renewal of human embryonic stem cells as revealed through a systems analysis of PI3K/AKT pathway.

Maintenance of the self-renewal state in human embryonic stem cells (hESCs) is the foremost critical step for regenerative therapy applications. The insulin-mediated PI3K/AKT pathway is well appreciated as being the central pathway supporting hESC self-renewal; however, the regulatory interactions in the pathway that maintain cell state are not yet known. Identification of these regulatory pathway components will be critical for designing targeted interventions to facilitate a completely defined platform for hESC propagation and differentiation. Here, we have developed a systems analysis approach to identify regulatory components that control PI3K/AKT pathway in self-renewing hESCs. A detailed mathematical model was adopted to explain the complex regulatory interactions in the PI3K/AKT pathway. We evaluated globally sensitive processes of the pathway in a computationally efficient manner by replacing the detailed model by a surrogate meta-model. Our mathematical analysis, supported by experimental validation, reveals that negative regulators of the molecules IRS1 and PIP3 primarily govern the steady state of the pathway in hESCs. Among the regulators, negative feedback via IRS1 reduces the sensitivity of various reactions associated with direct trunk of the pathway and also constraints the propagation of parameter uncertainty to the levels of post receptor signaling molecules. Furthermore, our results suggest that inhibition of negative feedback can significantly increase p-AKT levels and thereby, better support hESC self-renewal. Our integrated mathematical modeling and experimental workflow demonstrates the significant advantage of computationally efficient meta-model approaches to detect sensitive targets from signaling pathways. FORTRAN codes for the PI3K/AKT pathway and the RS-HDMR implementation are available from the authors upon request.