Hybrid modeling: towards the next level of scientific computing in engineering

Kurz, Stefan; Gersem, Herbert De; Galetzka, Armin; Klaedtke, Andreas; Liebsch, Melvin; Loukrezis, Dimitrios; Russenschuck, Stephan; Schmidt, Manuel

doi:10.1186/s13362-022-00123-0

Cited by 26 publications

(8 citation statements)

References 29 publications

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“…Hybrid models are somewhat in between process‐based and statistical models (in its wider sense, including classical statistics, statistical learning, data‐driven optimization, up to deep learning). These models combine first principle‐based models with data‐driven models into a joint architecture (Kurz et al., 2022) and aim at preserving some of the physical realism of process‐based models, while allowing for the flexibility, simplicity, and performance of data‐driven models. Hybrid models do not necessarily use more knowledge or data, but combine the benefits of process‐based and statistical models, placing them at a level equal to or below the highest data and knowledge use scenarios (Figure 5).…”

Section: Classification Of Lake Temperature Modelsmentioning

confidence: 99%

Lake Water Temperature Modeling in an Era of Climate Change: Data Sources, Models, and Future Prospects

Piccolroaz,

Zhu,

Ladwig

et al. 2024

Reviews of Geophysics

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Lake thermal dynamics have been considerably impacted by climate change, with potential adverse effects on aquatic ecosystems. To better understand the potential impacts of future climate change on lake thermal dynamics and related processes, the use of mathematical models is essential. In this study, we provide a comprehensive review of lake water temperature modeling. We begin by discussing the physical concepts that regulate thermal dynamics in lakes, which serve as a primer for the description of process‐based models. We then provide an overview of different sources of observational water temperature data, including in situ monitoring and satellite Earth observations, used in the field of lake water temperature modeling. We classify and review the various lake water temperature models available, and then discuss model performance, including commonly used performance metrics and optimization methods. Finally, we analyze emerging modeling approaches, including forecasting, digital twins, combining process‐based modeling with deep learning, evaluating structural model differences through ensemble modeling, adapted water management, and coupling of climate and lake models. This review is aimed at a diverse group of professionals working in the fields of limnology and hydrology, including ecologists, biologists, physicists, engineers, and remote sensing researchers from the private and public sectors who are interested in understanding lake water temperature modeling and its potential applications.

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Section: Classification Of Lake Temperature Modelsmentioning

confidence: 99%

Lake Water Temperature Modeling in an Era of Climate Change: Data Sources, Models, and Future Prospects

Piccolroaz,

Zhu,

Ladwig

et al. 2024

Reviews of Geophysics

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“…Kirchhoff's circuit laws are derived from Maxwell's equations, either in the low‐frequency limit or under the assumption that the wavelength in the AC case is large compared with the circuit. Albeit these assumptions, Kirchhoff's circuit laws are derived from first principles and the equations are accepted to be exact 1 . In contrast, the models representing the lumped elements are mostly empirically known, thus introducing errors and epistemic (model‐form) uncertainties arising from the modeling process 2 .…”

Section: Introductionmentioning

confidence: 99%

“…Albeit these assumptions, Kirchhoff's circuit laws are derived from first principles and the equations are accepted to be exact. 1 In contrast, the models representing the lumped elements are mostly empirically known, thus introducing errors and epistemic (model-form) uncertainties arising from the modeling process. 2 Very commonly, these models are obtained via data-fitting techniques, for example, based on physically motivated approaches 3,4 or sophisticated machine learning regression methods, [5][6][7] to name a few options.Nowadays, the availability of data increases steadily.…”

mentioning

confidence: 99%

Data‐driven model‐free modified nodal analysis circuit solver

Galetzka,

Loukrezis,

De Gersem

2024

Int J Numerical Modelling

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This work introduces a novel data‐driven model‐free modified nodal analysis (MNA) circuit solver. The solver is capable of handling circuit problems featuring elements for which solely measurement data are available. Rather than utilizing hard‐coded phenomenological model representations, the data‐driven MNA solver reformulates the circuit problem such that the solution is found by minimizing the distance between circuit states that fulfill Kirchhoff's laws, and states belonging to the measurement data. In this way, the formerly inevitable demand for model representations is eliminated, thus avoiding the introduction of related modeling errors and uncertainties. The proposed solver is applied to linear and nonlinear RC‐circuits and to a half‐wave rectifier.

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“…Te proposal of hybrid models is a potential efcient alternative for modelling and forecasting the volatility of stock markets because such models can account for a number of important features of fnancial series [2,5]. Hybrid models combine frst principle-based models with data-based models into a joint architecture, supporting enhanced model qualities, such as robustness and explainability [21].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Model for Stock Market Volatility

Agyarko

Frempong

Wiah

2023

Journal of Probability and Statistics

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Empirical evidence suggests that the traditional GARCH-type models are unable to accurately estimate the volatility of financial markets. To improve on the accuracy of the traditional GARCH-type models, a hybrid model (BSGARCH (1, 1)) that combines the flexibility of B-splines with the GARCH (1, 1) model has been proposed in the study. The lagged residuals from the GARCH (1, 1) model are fitted with a B-spline estimator and added to the results produced from the GARCH (1, 1) model. The proposed BSGARCH (1, 1) model was applied to simulated data and two real financial time series data (NASDAQ 100 and S&P 500). The outcome was then compared to the outcomes of the GARCH (1, 1), EGARCH (1, 1), GJR-GARCH (1, 1), and APARCH (1, 1) with different error distributions (ED) using the mean absolute percentage error (MAPE), the root mean square error (RMSE), Theil’s inequality coefficient (TIC) and QLIKE. It was concluded that the proposed BSGARCH (1, 1) model outperforms the traditional GARCH-type models that were considered in the study based on the performance metrics, and thus, it can be used for estimating volatility of stock markets.

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Hybrid modeling: towards the next level of scientific computing in engineering

Cited by 26 publications

References 29 publications

Lake Water Temperature Modeling in an Era of Climate Change: Data Sources, Models, and Future Prospects

Lake Water Temperature Modeling in an Era of Climate Change: Data Sources, Models, and Future Prospects

Data‐driven model‐free modified nodal analysis circuit solver

Hybrid Model for Stock Market Volatility

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