A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal ...A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition(POD),and low-dimensional data are used to train an autoencoder(AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori(MAP)-based objective for online reconstruction.The numerical results on the two-dimensional(2D) Bhatnagar-Gross-Krook-Boltzmann(BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition(Gappy POD), especially for the data with slowly decaying singular values,and is more efficient in training than gappy autoencoder(Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.展开更多
Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularl...Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.展开更多
In almost all previous works, the hyperbolic dispersion surfaces of the central proper quadrics have been crudely derived from the degree of reduction from the bi-quadratic equation by use of some roughly indefinable ...In almost all previous works, the hyperbolic dispersion surfaces of the central proper quadrics have been crudely derived from the degree of reduction from the bi-quadratic equation by use of some roughly indefinable approximate relations. Moreover, neglecting the high symmetry of the hyperbola, both the branches have been approximated on the asymmetric surfaces composed of a pair of a branch of the hyperbola and a vertex of the ellipse without the presentation of reasonable evidence. Based upon the same dispersion surfaces equation, a new original gapless dispersion surfaces could be rigorously introduced without crude omission of even a term in the bi-quadratic equation based upon usual analogy with the extended band theory of solid as the close approximation to the truth.展开更多
Digital twin is a cutting-edge technology in the energy industry,capable of predicting real-time operation data for equipment performance monitoring and operational optimization.However,methods for calibrating and fus...Digital twin is a cutting-edge technology in the energy industry,capable of predicting real-time operation data for equipment performance monitoring and operational optimization.However,methods for calibrating and fusing digital twin prediction with limited in-situ measured data are still lacking,especially for equipment involving complicated multiphase flow and chemical reactions like coal-fired boilers.In this work,using coal-fired boiler water wall temperature monitoring as an example,we propose a digital twin that reconstructs the water wall temperature distribution with high spatial resolution in real time and calibrates the reconstruction using in-situ water wall temperature data.The digital twin is established using the gappy proper orthogonal decomposition(POD)reduced-order model by fusing CFD solutions and measured data.The reconstruction accuracy of the digital twin was initially validated.And then,the minimum number of measured data sampling points required for precise reconstruction was investigated.An improved uniform data collection method was subsequently developed.After that,the computational time required for the digital twin and the traditional CFD was compared.Finally,the reconstruction method was further validated by in-situ measured temperature from the in-service boiler.Results indicate that the established digital twin can precisely reconstruct the water wall temperature in real time.Thirty-nine sampling points are sufficient to reconstruct the temperature distribution with the original data collection method.The proposed uniform data collection method further reduces the mean relative errors to less than 0.4%across four test cases,and with the constrained technique,the errors decrease to 0.374%and 0.345%for Cases 1 and 3,which had poor reconstructions using the original sampling point arrangement.In addition,the reconstruction time of the digital twin is also considerably reduced compared to CFD.Engineering application indicates that the reconstructed temperatures are highly consistent with in-situ measured data.The established water wall temperature digital twin is beneficial for water wall tube overheating detection and operation optimization.展开更多
基金supported by the National Natural Science Foundation of China(No.12472197)。
文摘A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition(POD),and low-dimensional data are used to train an autoencoder(AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori(MAP)-based objective for online reconstruction.The numerical results on the two-dimensional(2D) Bhatnagar-Gross-Krook-Boltzmann(BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition(Gappy POD), especially for the data with slowly decaying singular values,and is more efficient in training than gappy autoencoder(Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.
文摘Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.
文摘In almost all previous works, the hyperbolic dispersion surfaces of the central proper quadrics have been crudely derived from the degree of reduction from the bi-quadratic equation by use of some roughly indefinable approximate relations. Moreover, neglecting the high symmetry of the hyperbola, both the branches have been approximated on the asymmetric surfaces composed of a pair of a branch of the hyperbola and a vertex of the ellipse without the presentation of reasonable evidence. Based upon the same dispersion surfaces equation, a new original gapless dispersion surfaces could be rigorously introduced without crude omission of even a term in the bi-quadratic equation based upon usual analogy with the extended band theory of solid as the close approximation to the truth.
基金supported by the Scientific and Technological Innovation Project of Carbon Emission Peak and Carbon Neutrality of Jiangsu Province(BE2023854)the New Cornerstone Science Foundation through the XPLORER PRIZE。
文摘Digital twin is a cutting-edge technology in the energy industry,capable of predicting real-time operation data for equipment performance monitoring and operational optimization.However,methods for calibrating and fusing digital twin prediction with limited in-situ measured data are still lacking,especially for equipment involving complicated multiphase flow and chemical reactions like coal-fired boilers.In this work,using coal-fired boiler water wall temperature monitoring as an example,we propose a digital twin that reconstructs the water wall temperature distribution with high spatial resolution in real time and calibrates the reconstruction using in-situ water wall temperature data.The digital twin is established using the gappy proper orthogonal decomposition(POD)reduced-order model by fusing CFD solutions and measured data.The reconstruction accuracy of the digital twin was initially validated.And then,the minimum number of measured data sampling points required for precise reconstruction was investigated.An improved uniform data collection method was subsequently developed.After that,the computational time required for the digital twin and the traditional CFD was compared.Finally,the reconstruction method was further validated by in-situ measured temperature from the in-service boiler.Results indicate that the established digital twin can precisely reconstruct the water wall temperature in real time.Thirty-nine sampling points are sufficient to reconstruct the temperature distribution with the original data collection method.The proposed uniform data collection method further reduces the mean relative errors to less than 0.4%across four test cases,and with the constrained technique,the errors decrease to 0.374%and 0.345%for Cases 1 and 3,which had poor reconstructions using the original sampling point arrangement.In addition,the reconstruction time of the digital twin is also considerably reduced compared to CFD.Engineering application indicates that the reconstructed temperatures are highly consistent with in-situ measured data.The established water wall temperature digital twin is beneficial for water wall tube overheating detection and operation optimization.
