SMT 2.0: A Surrogate Modeling Toolbox with a focus on hierarchical and mixed variables Gaussian processes

Saves, Paul; Lafage, Rémi; Bartoli, Nathalie; Diouane, Youssef; Bussemaker, Jasper; Lefebvre, Thierry; Hwang, John T.; Morlier, Joseph; Martins, Joaquim R.R.A.

doi:10.1016/j.advengsoft.2023.103571

Cited by 14 publications

(5 citation statements)

References 56 publications

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“…The dynamic model is solved using off-the-shelf stiff solvers, such as Radau, BDF, and LSODA from the Scipy package in Python. For the data-driven analysis discussed in Section , we use the python’s Latin hypercube sampling technique from the Surrogate modeling toolbox package to generate 2000 data points in a five-dimensional parameter space ( E 1 , E 2 , T avg , A , and ω). The ranges scanned for the five parameters are E 1 and E 2 , 10 4 to 10 6 J/mol; T avg , 500 to 1200 K; A , 50 to 200 K; and ω, 10 –2 to 10 3 Hz.…”

Section: Methodsmentioning

confidence: 99%

Enhanced Performance of Dynamic Temperature Pulsing: Modeling Insights from Simple Reaction Networks

Railkar,

Vlachos

2023

Ind. Eng. Chem. Res.

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We develop a dynamic model with temperature as the control variable and simplified reaction networks to investigate the potential benefits of periodic pulse heating for endothermic gas-phase reactions. The results suggest that dynamic electrification of gas-phase reactions could substantially improve the conversion compared to steady-state heating for a first-order reversible endothermic reaction and overcome equilibrium limitations under certain conditions. Series and parallel reactions demonstrate improvement in yield at a high pulsing frequency and amplitude in a certain temperature range. A data-driven approach is introduced to classify conditions for the enhanced performance of nonlinear systems under periodic operation. These revelations underscore the promising potential of implementing a temperature pulse heating strategy in practical applications, leveraging the existing body of knowledge to achieve superior outcomes. Finally, we explain recent experimental results and propose systems in which such behavior could be observed.

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Section: Methodsmentioning

confidence: 99%

Enhanced Performance of Dynamic Temperature Pulsing: Modeling Insights from Simple Reaction Networks

Railkar,

Vlachos

2023

Ind. Eng. Chem. Res.

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“…SMT stands as a robust tool for surrogate modeling, optimization, and sensitivity analysis, offering a comprehensive set of features tailored for constructing data-driven models and leveraging them in various engineering applications [19,22]. With a user-friendly interface and online documentation, SMT aims to streamline the application of surrogate models in practical scenarios, making it accessible to practitioners.…”

Section: Surrogate Modeling Toolbox (Smt)mentioning

confidence: 99%

A Python Toolbox for Data-Driven Aerodynamic Modeling Using Sparse Gaussian Processes

Valayer,

Bartoli,

Castaño-Aguirre

et al. 2024

Aerospace

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In aerodynamics, characterizing the aerodynamic behavior of aircraft typically requires a large number of observation data points. Real experiments can generate thousands of data points with suitable accuracy, but they are time-consuming and resource-intensive. Consequently, conducting real experiments at new input configurations might be impractical. To address this challenge, data-driven surrogate models have emerged as a cost-effective and time-efficient alternative. They provide simplified mathematical representations that approximate the output of interest. Models based on Gaussian Processes (GPs) have gained popularity in aerodynamics due to their ability to provide accurate predictions and quantify uncertainty while maintaining tractable execution times. To handle large datasets, sparse approximations of GPs have been further investigated to reduce the computational complexity of exact inference. In this paper, we revisit and adapt two classic sparse methods for GPs to address the specific requirements frequently encountered in aerodynamic applications. We compare different strategies for choosing the inducing inputs, which significantly impact the complexity reduction. We formally integrate our implementations into the open-source Python toolbox SMT, enabling the use of sparse methods across the GP regression pipeline. We demonstrate the performance of our Sparse GP (SGP) developments in a comprehensive 1D analytic example as well as in a real wind tunnel application with thousands of training data points.

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“…In the test, the surrogate model 𝑓 𝑃𝐷𝐸𝑠 for nonlinear PDEs is built by the POD-ROM method where the RBF model is selected as the coefficient model. The SMT library (Saves et al, 2024) is adopted to implement RBF modeling with default settings.…”

Section: Data Preparationmentioning

confidence: 99%

“…To demonstrate the generality of the proposed online update and application method, KRG and ELM are selected for study. In the test, KRG and ELM are implemented by the SMT library (Saves et al, 2024) and the 𝑒𝑙𝑚 library (Li, 2018) respectively. For ELM, the number of hidden layers is set as 16 × (𝑛 𝑖𝑛 + 𝑘), where 𝑛 𝑖𝑛 and 𝑘 are the dimensions of the input 𝑥 and the corresponding coefficient vector respectively.…”

Section: Effects Of Coefficient Model Optionsmentioning

confidence: 99%

A Systematic Online Update Method for Reduced-Order-Model-Based Digital Twin

Tang,

Sajadi,

Dehaghani

et al. 2024

Preprint

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A digital twin (DT) is a model that mirrors a physical system and is continuously updated with real-time data from the physical system. Recent implementations of reduced-order-model-based DT (DT-ROM) have been applied in aerodynamics and structural health monitoring, where partial differential equations (PDEs) are utilized to update reduced bases and coefficients. However, these methods are not directly applicable when the PDEs of the system are unknown. This paper addresses the online update challenge for DT-ROM in scenarios lacking known PDEs of the system. To tackle the challenge, a systematic online update and application method is proposed. During the online update, the projection residual of online data on the reduced bases determines the necessity of updating reduced bases, while the prediction residual of online data obtained by the current DT-ROM is used to decide whether to update the coefficient model. By sequentially evaluating both criteria, the method selectively incorporates essential online data for the online DT model update. During the online application, a criterion defined based on online data is adopted to determine whether the offline DT-ROM or the online one is applied to output final predictions. The capability of the proposed method is tested through three numerical and three engineering problems. Results indicate that the proposed online update method consistently reduces both projection and prediction residuals, thereby progressively enhancing the performance of the online DT-ROM on test data. Meanwhile, the online application method provides a prediction performance better than using offline DT-ROM only. Both demonstrate that the proposed work could be applied to online DT update where the PDEs of the system are unknown.

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SMT 2.0: A Surrogate Modeling Toolbox with a focus on hierarchical and mixed variables Gaussian processes

Cited by 14 publications

References 56 publications

Enhanced Performance of Dynamic Temperature Pulsing: Modeling Insights from Simple Reaction Networks

Enhanced Performance of Dynamic Temperature Pulsing: Modeling Insights from Simple Reaction Networks

A Python Toolbox for Data-Driven Aerodynamic Modeling Using Sparse Gaussian Processes

A Systematic Online Update Method for Reduced-Order-Model-Based Digital Twin

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