D. Carter, Francis De Voogt, R. Soares, B. Ganapathisubramani
Abstract Recent work has demonstrated the use of sparse sensors in combination with the proper orthogonal decomposition (POD) to produce data-driven reconstructions of the full velocity fields in a variety of flows. The present work investigates the fidelity of such techniques applied to a stalled NACA 0012 aerofoil at $ {Re}_c=75,000 $ at an angle of attack $ alpha ={12}^{circ } $ as measured experimentally using planar time-resolved particle image velocimetry. In contrast to many previous studies, the flow is absent of any dominant shedding frequency and exhibits a broad range of singular values due to the turbulence in the separated region. Several reconstruction methodologies for linear state estimation based on classical compressed sensing and extended POD methodologies are presented as well as nonlinear refinement through the use of a shallow neural network (SNN). It is found that the linear reconstructions inspired by the extended POD are inferior to the compressed sensing approach provided that the sparse sensors avoid regions of the flow with small variance across the global POD basis. Regardless of the linear method used, the nonlinear SNN gives strikingly similar performance in its refinement of the reconstructions. The capability of sparse sensors to reconstruct separated turbulent flow measurements is further discussed and directions for future work suggested. Impact Statement Sparse reconstruction of full-field information using a limited subset of data is widely relevant to data-centric engineering applications; from reconstructing human faces with limited pixels to predicting laminar and turbulent flow fields from limited sensors. The focus of the present study is of the latter example with high relevance to active flow control in aerospace and related industry. There are multiple data-driven methodologies for obtaining flow field reconstructions from sparse measurements ranging from the linear unsupervised proper orthogonal decomposition to the use of nonlinear supervised NNs. The feasibility of such methods to flow fields that are highly turbulent as well as obtained via experiment remains an open area of research. The present study reveals the capability of these techniques to create a time-invariant library that can predict instantaneous states of the flow from sparse measurements alone (provided that these states are within the bounds of the applied training data). The proposed linear methods, as well as the NN architecture, provide well-characterized frameworks for future efforts in sparse sensing and state estimation applications: particularly for highly nonlinear underlying systems such as turbulent flow.
{"title":"Data-driven sparse reconstruction of flow over a stalled aerofoil using experimental data","authors":"D. Carter, Francis De Voogt, R. Soares, B. Ganapathisubramani","doi":"10.1017/dce.2021.5","DOIUrl":"https://doi.org/10.1017/dce.2021.5","url":null,"abstract":"Abstract Recent work has demonstrated the use of sparse sensors in combination with the proper orthogonal decomposition (POD) to produce data-driven reconstructions of the full velocity fields in a variety of flows. The present work investigates the fidelity of such techniques applied to a stalled NACA 0012 aerofoil at $ {Re}_c=75,000 $ at an angle of attack $ alpha ={12}^{circ } $ as measured experimentally using planar time-resolved particle image velocimetry. In contrast to many previous studies, the flow is absent of any dominant shedding frequency and exhibits a broad range of singular values due to the turbulence in the separated region. Several reconstruction methodologies for linear state estimation based on classical compressed sensing and extended POD methodologies are presented as well as nonlinear refinement through the use of a shallow neural network (SNN). It is found that the linear reconstructions inspired by the extended POD are inferior to the compressed sensing approach provided that the sparse sensors avoid regions of the flow with small variance across the global POD basis. Regardless of the linear method used, the nonlinear SNN gives strikingly similar performance in its refinement of the reconstructions. The capability of sparse sensors to reconstruct separated turbulent flow measurements is further discussed and directions for future work suggested. Impact Statement Sparse reconstruction of full-field information using a limited subset of data is widely relevant to data-centric engineering applications; from reconstructing human faces with limited pixels to predicting laminar and turbulent flow fields from limited sensors. The focus of the present study is of the latter example with high relevance to active flow control in aerospace and related industry. There are multiple data-driven methodologies for obtaining flow field reconstructions from sparse measurements ranging from the linear unsupervised proper orthogonal decomposition to the use of nonlinear supervised NNs. The feasibility of such methods to flow fields that are highly turbulent as well as obtained via experiment remains an open area of research. The present study reveals the capability of these techniques to create a time-invariant library that can predict instantaneous states of the flow from sparse measurements alone (provided that these states are within the bounds of the applied training data). The proposed linear methods, as well as the NN architecture, provide well-characterized frameworks for future efforts in sparse sensing and state estimation applications: particularly for highly nonlinear underlying systems such as turbulent flow.","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/dce.2021.5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43448134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Feature extraction and artificial neural networks for the on-the-fly classification of high-dimensional thermochemical spaces in adaptive-chemistry simulations – ERRATUM","authors":"G. D’Alessio, A. Cuoci, A. Parente","doi":"10.1017/dce.2021.4","DOIUrl":"https://doi.org/10.1017/dce.2021.4","url":null,"abstract":"","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/dce.2021.4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48660539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Reproducibility of a deep-learning fully convolutional neural network is evaluated by training several times the same network on identical conditions (database, hyperparameters, and hardware) with nondeterministic graphics processing unit operations. The network is trained to model three typical time–space-evolving physical systems in two dimensions: heat, Burgers’, and wave equations. The behavior of the networks is evaluated on both recursive and nonrecursive tasks. Significant changes in models’ properties (weights and feature fields) are observed. When tested on various benchmarks, these models systematically return estimations with a high level of deviation, especially for the recurrent analysis which strongly amplifies variability due to the nondeterminism. Trainings performed with double floating-point precision provide slightly better estimations and a significant reduction of the variability of both the network parameters and its testing error range.
{"title":"On the reproducibility of fully convolutional neural networks for modeling time–space-evolving physical systems","authors":"Wagner G. Pinto, Antonio Alguacil, M. Bauerheim","doi":"10.1017/dce.2022.18","DOIUrl":"https://doi.org/10.1017/dce.2022.18","url":null,"abstract":"Abstract Reproducibility of a deep-learning fully convolutional neural network is evaluated by training several times the same network on identical conditions (database, hyperparameters, and hardware) with nondeterministic graphics processing unit operations. The network is trained to model three typical time–space-evolving physical systems in two dimensions: heat, Burgers’, and wave equations. The behavior of the networks is evaluated on both recursive and nonrecursive tasks. Significant changes in models’ properties (weights and feature fields) are observed. When tested on various benchmarks, these models systematically return estimations with a high level of deviation, especially for the recurrent analysis which strongly amplifies variability due to the nondeterminism. Trainings performed with double floating-point precision provide slightly better estimations and a significant reduction of the variability of both the network parameters and its testing error range.","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47807129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Neural networks-based learning of the distribution of non-dispatchable renewable electricity generation from sources, such as photovoltaics (PV) and wind as well as load demands, has recently gained attention. Normalizing flow density models are particularly well suited for this task due to the training through direct log-likelihood maximization. However, research from the field of image generation has shown that standard normalizing flows can only learn smeared-out versions of manifold distributions. Previous works on normalizing flow-based scenario generation do not address this issue, and the smeared-out distributions result in the sampling of noisy time series. In this paper, we exploit the isometry of the principal component analysis (PCA), which sets up the normalizing flow in a lower-dimensional space while maintaining the direct and computationally efficient likelihood maximization. We train the resulting principal component flow (PCF) on data of PV and wind power generation as well as load demand in Germany in the years 2013–2015. The results of this investigation show that the PCF preserves critical features of the original distributions, such as the probability density and frequency behavior of the time series. The application of the PCF is, however, not limited to renewable power generation but rather extends to any dataset, time series, or otherwise, which can be efficiently reduced using PCA.
{"title":"Principal component density estimation for scenario generation using normalizing flows","authors":"Eike Cramer, A. Mitsos, R. Tempone, M. Dahmen","doi":"10.1017/dce.2022.7","DOIUrl":"https://doi.org/10.1017/dce.2022.7","url":null,"abstract":"Abstract Neural networks-based learning of the distribution of non-dispatchable renewable electricity generation from sources, such as photovoltaics (PV) and wind as well as load demands, has recently gained attention. Normalizing flow density models are particularly well suited for this task due to the training through direct log-likelihood maximization. However, research from the field of image generation has shown that standard normalizing flows can only learn smeared-out versions of manifold distributions. Previous works on normalizing flow-based scenario generation do not address this issue, and the smeared-out distributions result in the sampling of noisy time series. In this paper, we exploit the isometry of the principal component analysis (PCA), which sets up the normalizing flow in a lower-dimensional space while maintaining the direct and computationally efficient likelihood maximization. We train the resulting principal component flow (PCF) on data of PV and wind power generation as well as load demand in Germany in the years 2013–2015. The results of this investigation show that the PCF preserves critical features of the original distributions, such as the probability density and frequency behavior of the time series. The application of the PCF is, however, not limited to renewable power generation but rather extends to any dataset, time series, or otherwise, which can be efficiently reduced using PCA.","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46938143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The integration of Artificial Neural Networks (ANNs) and Feature Extraction (FE) in the context of the Sample- Partitioning Adaptive Reduced Chemistry approach was investigated in this work, to increase the on-the-fly classification accuracy for very large thermochemical states. The proposed methodology was firstly compared with an on-the-fly classifier based on the Principal Component Analysis reconstruction error, as well as with a standard ANN (s-ANN) classifier, operating on the full thermochemical space, for the adaptive simulation of a steady laminar flame fed with a nitrogen-diluted stream of n-heptane in air. The numerical simulations were carried out with a kinetic mechanism accounting for 172 species and 6,067 reactions, which includes the chemistry of Polycyclic Aromatic Hydrocarbons (PAHs) up to C$ {}_{20} $. Among all the aforementioned classifiers, the one exploiting the combination of an FE step with ANN proved to be more efficient for the classification of high-dimensional spaces, leading to a higher speed-up factor and a higher accuracy of the adaptive simulation in the description of the PAH and soot-precursor chemistry. Finally, the investigation of the classifier’s performances was also extended to flames with different boundary conditions with respect to the training one, obtained imposing a higher Reynolds number or time-dependent sinusoidal perturbations. Satisfying results were observed on all the test flames. Impact Statement The existing methodologies for the simulation of multidimensional flames with detailed kinetic mechanisms are time-consuming because of the large number of involved chemical species and reactions. This aspect has prompted the development of approaches to reduce the computational requirements of computational fluid dynamics simulations of reacting flows. Among them, adaptive chemistry is worth mentioning, as it allows to use complex kinetic mechanisms only where needed. In this work, an artificial neural network architecture with a prior encoding step via Principal Component Analysis was integrated in the Sample-Partitioning Adaptive Reduced Chemistry approach, to increase the on-the-fly classification accuracy when high-dimensional spaces are considered. Its performances were compared with others supervised classifiers, operating on the full thermochemical space, in terms of speed-up with respect to the detailed simulation and accuracy in the description of Polycyclic Aromatic Hydrocarbon species.
{"title":"Feature extraction and artificial neural networks for the on-the-fly classification of high-dimensional thermochemical spaces in adaptive-chemistry simulations","authors":"G. D’Alessio, A. Cuoci, A. Parente","doi":"10.1017/dce.2021.2","DOIUrl":"https://doi.org/10.1017/dce.2021.2","url":null,"abstract":"Abstract The integration of Artificial Neural Networks (ANNs) and Feature Extraction (FE) in the context of the Sample- Partitioning Adaptive Reduced Chemistry approach was investigated in this work, to increase the on-the-fly classification accuracy for very large thermochemical states. The proposed methodology was firstly compared with an on-the-fly classifier based on the Principal Component Analysis reconstruction error, as well as with a standard ANN (s-ANN) classifier, operating on the full thermochemical space, for the adaptive simulation of a steady laminar flame fed with a nitrogen-diluted stream of n-heptane in air. The numerical simulations were carried out with a kinetic mechanism accounting for 172 species and 6,067 reactions, which includes the chemistry of Polycyclic Aromatic Hydrocarbons (PAHs) up to C$ {}_{20} $. Among all the aforementioned classifiers, the one exploiting the combination of an FE step with ANN proved to be more efficient for the classification of high-dimensional spaces, leading to a higher speed-up factor and a higher accuracy of the adaptive simulation in the description of the PAH and soot-precursor chemistry. Finally, the investigation of the classifier’s performances was also extended to flames with different boundary conditions with respect to the training one, obtained imposing a higher Reynolds number or time-dependent sinusoidal perturbations. Satisfying results were observed on all the test flames. Impact Statement The existing methodologies for the simulation of multidimensional flames with detailed kinetic mechanisms are time-consuming because of the large number of involved chemical species and reactions. This aspect has prompted the development of approaches to reduce the computational requirements of computational fluid dynamics simulations of reacting flows. Among them, adaptive chemistry is worth mentioning, as it allows to use complex kinetic mechanisms only where needed. In this work, an artificial neural network architecture with a prior encoding step via Principal Component Analysis was integrated in the Sample-Partitioning Adaptive Reduced Chemistry approach, to increase the on-the-fly classification accuracy when high-dimensional spaces are considered. Its performances were compared with others supervised classifiers, operating on the full thermochemical space, in terms of speed-up with respect to the detailed simulation and accuracy in the description of Polycyclic Aromatic Hydrocarbon species.","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/dce.2021.2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41836917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We explore the concept of parameter design applied to the production of glass beads in the manufacture of metal-encapsulated transistors. The main motivation is to complete the analysis hinted at in the original publication by Jim Morrison in 1957, which was an early example of discussing the idea of transmitted variation in engineering design, and an influential paper in the development of analytic parameter design as a data-centric engineering activity. Parameter design is a secondary design activity focused on selecting the nominals of the design variables to achieve the required target performance and to simultaneously reduce the variance around the target. Although the 1957 paper is not recent, its approach to engineering design is modern. Impact Statement This paper draws attention to a 1957 publication by Jim Morrison and illustrates the concept of parameter design (a secondary design activity between concept design and tolerance design). The 1957 paper was the first in the English language to discuss parameter design and is an early example of data-centric engineering. This paper illustrates that the obvious or intuitive solutions to design optimization can be wrong, even in the simplest of cases as illustrated here, motivating the need for careful data-centered analysis, when solving engineering problems.
{"title":"The study of variability in engineering design—An appreciation and a retrospective","authors":"T. Davis","doi":"10.1017/dce.2021.3","DOIUrl":"https://doi.org/10.1017/dce.2021.3","url":null,"abstract":"Abstract We explore the concept of parameter design applied to the production of glass beads in the manufacture of metal-encapsulated transistors. The main motivation is to complete the analysis hinted at in the original publication by Jim Morrison in 1957, which was an early example of discussing the idea of transmitted variation in engineering design, and an influential paper in the development of analytic parameter design as a data-centric engineering activity. Parameter design is a secondary design activity focused on selecting the nominals of the design variables to achieve the required target performance and to simultaneously reduce the variance around the target. Although the 1957 paper is not recent, its approach to engineering design is modern. Impact Statement This paper draws attention to a 1957 publication by Jim Morrison and illustrates the concept of parameter design (a secondary design activity between concept design and tolerance design). The 1957 paper was the first in the English language to discuss parameter design and is an early example of data-centric engineering. This paper illustrates that the obvious or intuitive solutions to design optimization can be wrong, even in the simplest of cases as illustrated here, motivating the need for careful data-centered analysis, when solving engineering problems.","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/dce.2021.3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47483669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Eky Febrianto, Liam J. Butler, M. Girolami, F. Cirak
Abstract The monitoring of infrastructure assets using sensor networks is becoming increasingly prevalent. A digital twin in the form of a finite element (FE) model, as commonly used in design and construction, can help make sense of the copious amount of collected sensor data. This paper demonstrates the application of the statistical finite element method (statFEM), which provides a principled means of synthesizing data and physics-based models, in developing a digital twin of a self-sensing structure. As a case study, an instrumented steel railway bridge of $ 27.34hskip1.5pt mathrm{m} $ length located along the West Coast Mainline near Staffordshire in the UK is considered. Using strain data captured from fiber Bragg grating sensors at 108 locations along the bridge superstructure, statFEM can predict the “true” system response while taking into account the uncertainties in sensor readings, applied loading, and FE model misspecification errors. Longitudinal strain distributions along the two main I-beams are both measured and modeled during the passage of a passenger train. The statFEM digital twin is able to generate reasonable strain distribution predictions at locations where no measurement data are available, including at several points along the main I-beams and on structural elements on which sensors are not even installed. The implications for long-term structural health monitoring and assessment include optimization of sensor placement and performing more reliable what-if analyses at locations and under loading scenarios for which no measurement data are available.
{"title":"Digital twinning of self-sensing structures using the statistical finite element method","authors":"Eky Febrianto, Liam J. Butler, M. Girolami, F. Cirak","doi":"10.1017/dce.2022.28","DOIUrl":"https://doi.org/10.1017/dce.2022.28","url":null,"abstract":"Abstract The monitoring of infrastructure assets using sensor networks is becoming increasingly prevalent. A digital twin in the form of a finite element (FE) model, as commonly used in design and construction, can help make sense of the copious amount of collected sensor data. This paper demonstrates the application of the statistical finite element method (statFEM), which provides a principled means of synthesizing data and physics-based models, in developing a digital twin of a self-sensing structure. As a case study, an instrumented steel railway bridge of $ 27.34hskip1.5pt mathrm{m} $ length located along the West Coast Mainline near Staffordshire in the UK is considered. Using strain data captured from fiber Bragg grating sensors at 108 locations along the bridge superstructure, statFEM can predict the “true” system response while taking into account the uncertainties in sensor readings, applied loading, and FE model misspecification errors. Longitudinal strain distributions along the two main I-beams are both measured and modeled during the passage of a passenger train. The statFEM digital twin is able to generate reasonable strain distribution predictions at locations where no measurement data are available, including at several points along the main I-beams and on structural elements on which sensors are not even installed. The implications for long-term structural health monitoring and assessment include optimization of sensor placement and performing more reliable what-if analyses at locations and under loading scenarios for which no measurement data are available.","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48740222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily extended to flow configurations where the transition process depends on a large set of parameters. In comparison, neural network methods allow higher dimensional input features to be considered without compromising the efficiency and accuracy of the traditional data-driven models. Neural network methods proposed earlier follow a cumbersome methodology of predicting instability growth rates over a broad range of frequencies, which are then processed to obtain the N-factor envelope, and then, the transition location based on the correlating N-factor. This paper presents an end-to-end transition model based on a recurrent neural network, which sequentially processes the mean boundary-layer profiles along the surface of the aerodynamic body to directly predict the N-factor envelope and the transition locations over a two-dimensional airfoil. The proposed transition model has been developed and assessed using a large database of 53 airfoils over a wide range of chord Reynolds numbers and angles of attack. The large universe of airfoils encountered in various applications causes additional difficulties. As such, we provide further insights on selecting training datasets from large amounts of available data. Although the proposed model has been analyzed for two-dimensional boundary layers in this paper, it can be easily generalized to other flows due to embedded feature extraction capability of convolutional neural network in the model.
{"title":"Recurrent neural network for end-to-end modeling of laminar-turbulent transition","authors":"M. Zafar, Meelan Choudhari, P. Paredes, Heng Xiao","doi":"10.1017/dce.2021.11","DOIUrl":"https://doi.org/10.1017/dce.2021.11","url":null,"abstract":"Abstract Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily extended to flow configurations where the transition process depends on a large set of parameters. In comparison, neural network methods allow higher dimensional input features to be considered without compromising the efficiency and accuracy of the traditional data-driven models. Neural network methods proposed earlier follow a cumbersome methodology of predicting instability growth rates over a broad range of frequencies, which are then processed to obtain the N-factor envelope, and then, the transition location based on the correlating N-factor. This paper presents an end-to-end transition model based on a recurrent neural network, which sequentially processes the mean boundary-layer profiles along the surface of the aerodynamic body to directly predict the N-factor envelope and the transition locations over a two-dimensional airfoil. The proposed transition model has been developed and assessed using a large database of 53 airfoils over a wide range of chord Reynolds numbers and angles of attack. The large universe of airfoils encountered in various applications causes additional difficulties. As such, we provide further insights on selecting training datasets from large amounts of available data. Although the proposed model has been analyzed for two-dimensional boundary layers in this paper, it can be easily generalized to other flows due to embedded feature extraction capability of convolutional neural network in the model.","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41315390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Qinyu Zhuang, Juan M Lorenzi, H. Bungartz, D. Hartmann
Abstract Model order reduction (MOR) methods enable the generation of real-time-capable digital twins, with the potential to unlock various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems, incorporating machine learning to deal with nonlinearity becomes a new choice for reducing complex problems. These kinds of methods are independent to the numerical solver for the full order model and keep the nonintrusiveness of the whole workflow. Such methods usually consist of two steps. The first step is the dimension reduction by a projection-based method, and the second is the model reconstruction by a neural network (NN). In this work, we apply some modifications for both steps respectively and investigate how they are impacted by testing with three different simulation models. In all cases Proper orthogonal decomposition is used for dimension reduction. For this step, the effects of generating the snapshot database with constant input parameters is compared with time-dependent input parameters. For the model reconstruction step, three types of NN architectures are compared: multilayer perceptron (MLP), explicit Euler NN (EENN), and Runge–Kutta NN (RKNN). The MLPs learn the system state directly, whereas EENNs and RKNNs learn the derivative of system state and predict the new state as a numerical integrator. In the tests, RKNNs show their advantage as the network architecture informed by higher-order numerical strategy.
{"title":"Model order reduction based on Runge–Kutta neural networks","authors":"Qinyu Zhuang, Juan M Lorenzi, H. Bungartz, D. Hartmann","doi":"10.1017/dce.2021.15","DOIUrl":"https://doi.org/10.1017/dce.2021.15","url":null,"abstract":"Abstract Model order reduction (MOR) methods enable the generation of real-time-capable digital twins, with the potential to unlock various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems, incorporating machine learning to deal with nonlinearity becomes a new choice for reducing complex problems. These kinds of methods are independent to the numerical solver for the full order model and keep the nonintrusiveness of the whole workflow. Such methods usually consist of two steps. The first step is the dimension reduction by a projection-based method, and the second is the model reconstruction by a neural network (NN). In this work, we apply some modifications for both steps respectively and investigate how they are impacted by testing with three different simulation models. In all cases Proper orthogonal decomposition is used for dimension reduction. For this step, the effects of generating the snapshot database with constant input parameters is compared with time-dependent input parameters. For the model reconstruction step, three types of NN architectures are compared: multilayer perceptron (MLP), explicit Euler NN (EENN), and Runge–Kutta NN (RKNN). The MLPs learn the system state directly, whereas EENNs and RKNNs learn the derivative of system state and predict the new state as a numerical integrator. In the tests, RKNNs show their advantage as the network architecture informed by higher-order numerical strategy.","PeriodicalId":34169,"journal":{"name":"DataCentric Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42433722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Saptarshi Das, M. Hobson, F. Feroz, Xi Chen, S. Phadke, J. Goudswaard, D. Hohl
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. Impact Statement Bayesian evidence-based reasoning is helpful in identifying real microseismic events as opposed to the environmental noise. The geophysical challenge here is the high-computational burden for simulating noiseless template seismic responses for explosive type events and combining them together having different amplitudes and origin times. We use Gaussian process based surrogate models as proxy for multi-receiver seismic responses to be used for the Bayesian detection of microseismic events in a heterogeneous marine velocity model. We used the MultiNest sampler for Bayesian inference since in the presence of multiple events, the likelihood surface becomes multimodal. From the sampled points, a density-based clustering algorithm is employed to filter out each microseismic event for improved mode separation and obtain the posterior distribution of each event in a joint 5D space of amplitude, origin time, and three spatial co-ordinates. Choice of the resolution parameter in MultiNest sampler (Nlive) is also crucial to obtain accurate inference within reasonable computational time and resources and have been compared for two different scenarios (Nlive = 300, 500). A data analytics pipeline is proposed in this paper, starting from GPU based simulation of microseismic events to training a surrogate model for cheaper likelihood calculation, followed by 5D posterior inference for simultaneous detection
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