7 Data-driven methods for reduced-order modeling

Brunton, Steven L.; Kutz, J. Nathan

doi:10.1515/9783110671490-007

Cited by 4 publications

(2 citation statements)

References 131 publications

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“…Secondly, these models will be transformed into the low order models, by math transforms, such as projection, optimal Hankel norm approximation, or Krylov methods. More recently, a new suggestion has emerged as 'data driven order reduction', which does not need to go over a high dimension model firstly, as it can be seen with more details in reference [25].…”

Section: Lower Order Modelsmentioning

confidence: 99%

Application of Data Science in the Sustainable Energy Industry

Marques¹

2022

Uncertainty Modeling: Fundamental Concepts and Models

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The application of Data Science (DS) in engineering fields is presented from a broad approach, taking the basics and historical motivation to apply statistical tools into practical needs, from Health Sciences to structural monitoring, the latter linked to the sustainable energy context, like solar, wind, geothermal and nuclear. Moreover, brief bullets about the DS techniques and models are also covered, most in the Machine Learning branch, but with some indications of Artificial Intelligence applications. Math techniques like Kringing, Support Vector Machines, Cross-Validation, Data Regularization, Surrogate Models, for instance, also make part of the text, where the practical issues are evaluated in a brief technical manner. The chapter covers the structural reliability and its DS application too.

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Section: Lower Order Modelsmentioning

confidence: 99%

Application of Data Science in the Sustainable Energy Industry

Marques¹

2022

Uncertainty Modeling: Fundamental Concepts and Models

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“…Following e.g. [55], we compute the Singular Value Decomposition of a "tall" simulation matrix 𝑋 ∈ R 𝑝×𝑞 (spatial points × time-steps):…”

Section: Pod Comparison Of Fnn and Lstm Predictionsmentioning

confidence: 99%

Deep learning for surrogate modelling of 2D mantle convection

Agarwal,

Tosi,

Kessel

et al. 2021

Preprint

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Mantle convection, the buoyancy-driven creeping flow of silicate rocks in the interior of terrestrial planets like Earth, Mars, Mercury and Venus, plays a fundamental role in the long-term thermal evolution of these bodies. Yet, key parameters and initial conditions of the partial differential equations governing mantle convection are poorly constrained. This often requires a large sampling of the parameter space to determine which combinations can satisfy certain observational constraints. Traditionally, 1D models based on scaling laws used to parameterized convective heat transfer, have been used to tackle the computational bottleneck of high-fidelity forward runs in 2D or 3D. However, these are limited in the amount of physics they can model (e.g. depth dependent material properties) and predict only mean quantities such as the mean mantle temperature. A recent machine learning study has shown that feedforward neural networks (FNN) trained using a large number of 2D simulations can overcome this limitation and reliably predict the evolution of entire 1D laterally-averaged temperature profile in time for complex models [1]. We now extend that approach to predict the full 2D temperature field, which contains more information in the form of convection structures such as hot plumes and cold downwellings. Using a dataset of 10, 525 two-dimensional simulations of the thermal evolution of the mantle of a Mars-like planet, we show that deep learning techniques can produce reliable parameterized surrogates (i.e. surrogates that predict state variables such as temperature based only on parameters) of the underlying partial differential equations. We first use convolutional autoencoders to compress the temperature fields by a factor of 142 and then use FNN and long-short term memory networks (LSTM) to predict the compressed fields. On average, the FNN predictions are 99.30% and the LSTM predictions are 99.22% accurate with respect to unseen simulations. Proper orthogonal decomposition (POD) of the LSTM and FNN predictions shows that despite a lower mean absolute relative accuracy, LSTMs capture the flow dynamics better than FNNs. When summed, the POD coefficients from FNN predictions and from LSTM predictions amount to 96.51% and 97.66% relative to the coefficients of the original simulations, respectively. I. INTRODUCTIONStudying the long-term thermal evolution of terrestrial planets like Earth, Venus, Mercury and Mars requires detailed modelling of thermal convection in their rocky mantles (e.g., [2]). Similar

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Towards the Salinity Profile Influence on an Internal Wave Attractor Formation

Elistratov,

But

2024

Water Waves

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7 Data-driven methods for reduced-order modeling

Cited by 4 publications

References 131 publications

Application of Data Science in the Sustainable Energy Industry

Application of Data Science in the Sustainable Energy Industry

Deep learning for surrogate modelling of 2D mantle convection

Towards the Salinity Profile Influence on an Internal Wave Attractor Formation

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