Deep learning method is of great importance in solving partial differential equations.In this paper,inspired by the failure-informed idea proposed by Gao et al.(SIAM Journal on Scientific Computing 45(4)(2023))and as ...Deep learning method is of great importance in solving partial differential equations.In this paper,inspired by the failure-informed idea proposed by Gao et al.(SIAM Journal on Scientific Computing 45(4)(2023))and as an improvement,a new accurate adaptive deep learning method is proposed for solving elliptic problems,including interface problems and convection-dominated problems.Based on the failure probability framework,the piece-wise uniform distribution is used to approximate the optimal proposal distribution and a kernel-based method is proposed for efficient sampling.Together with the improved Levenberg-Marquardt optimization method,the proposed adaptive deep learning method shows great potential in improving solution accuracy.Numerical tests on the elliptic problems without interface conditions,on one elliptic interface problem,and on the convection-dominated problems demonstrate the effectiveness of the proposed method,as it reduces the relative errors by a factor varying from 102 to 104 for different cases.展开更多
X-ray absorption near edge structure(XANES)spectroscopy is a powerful technique for characterizing the chemical state andsymmetry of individual elements within materials,but requires collecting data at many energy poi...X-ray absorption near edge structure(XANES)spectroscopy is a powerful technique for characterizing the chemical state andsymmetry of individual elements within materials,but requires collecting data at many energy points which can be time-consuming.While adaptive sampling methods exist for efficiently collecting spectroscopic data,they often lack domain-specific knowledge about the structure of XANES spectra.Here we demonstrate a knowledge-injected Bayesian optimization approach for adaptive XANES data collection that incorporates understanding of spectral features like absorption edges and pre-edge peaks.We show this method accurately reconstructs the absorption edge of XANES spectra using only 15–20%of the measurement points typically needed for conventional sampling,while maintaining the ability to determine the x-ray energy of the sharp peak after the absorption edge with errors less than 0.03 eV,the absorption edge with errors less than 0.1 eV;and overall root-mean-square errors less than 0.005 compared to traditionally sampled spectra.Our experiments on battery materials and catalysts demonstrate the method’s effectiveness for both static and dynamic XANES measurements,improving data collection efficiency and enabling better time resolution for tracking chemical changes.This approach advances the degree of automation in XANES experiments,reducing the common errors of under-or over-sampling points near the absorption edge and enabling dynamic experiments that require high temporal resolution or limited measurement time.展开更多
.A non-intrusive reduced order model(ROM)that combines a proper orthogonal decomposition(POD)and an artificial neural network(ANN)is primarily studied to investigate the applicability of the proposed ROM in recovering....A non-intrusive reduced order model(ROM)that combines a proper orthogonal decomposition(POD)and an artificial neural network(ANN)is primarily studied to investigate the applicability of the proposed ROM in recovering the solutions with shocks and strong gradients accurately and resolving fine-scale structures efficiently for hyperbolic conservation laws.Its accuracy is demonstrated by solving a high-dimensional parametrized ODE and the one-dimensional viscous Burgers’equation with a parameterized diffusion coefficient.The two-dimensional singlemode Rayleigh-Taylor instability(RTI),where the amplitude of the small perturbation and time are considered as free parameters,is also simulated.An adaptive sampling method in time during the linear regime of the RTI is designed to reduce the number of snapshots required for POD and the training of ANN.The extensive numerical results show that the ROM can achieve an acceptable accuracy with improved efficiency in comparison with the standard full order method.展开更多
Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelih...Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelihood function of the Bayesian method is commonly computationally expensive or analytically unavailable.In this study,in order to circumvent this intractable likelihood function,the approximate Bayesian computation(ABC)is expanded to the IHCPs.In ABC,the high dimensional observations in the intractable likelihood function are equalized by their low dimensional summary statistics.Thus,the performance of the ABC depends on the selection of summary statistics.In this study,a machine learning-based ABC(ML-ABC)is proposed to address the complicated selections of the summary statistics.The Auto-Encoder(AE)is a powerful Machine Learning(ML)framework which can compress the observations into very low dimensional summary statistics with little information loss.In addition,in order to accelerate the calculation of the proposed framework,another neural network(NN)is utilized to construct the mapping between the unknowns and the summary statistics.With this mapping,given arbitrary unknowns,the summary statistics can be obtained efficiently without solving the time-consuming forward problem with numerical method.Furthermore,an adaptive nested sampling method(ANSM)is developed to further improve the efficiency of sampling.The performance of the proposed method is demonstrated with two IHCP cases.展开更多
基金supported by the Natural Science Foundation of Hunan Province(Grant No.2023JJ30648)the Natural Science Foundation of Changsha(Grant No.kq2208252)+3 种基金supported by the Excellent Youth Foundation of Education Bureau of Hunan Province(Grant No.21B0301)the Natural Science Foundation of Hunan Province(Grant No.2022JJ40461)supported by the Natural Science Foundation of China(Grant No.12101615)the Natural Science Foundation of Hunan Province(Grant No.2022JJ40567).
文摘Deep learning method is of great importance in solving partial differential equations.In this paper,inspired by the failure-informed idea proposed by Gao et al.(SIAM Journal on Scientific Computing 45(4)(2023))and as an improvement,a new accurate adaptive deep learning method is proposed for solving elliptic problems,including interface problems and convection-dominated problems.Based on the failure probability framework,the piece-wise uniform distribution is used to approximate the optimal proposal distribution and a kernel-based method is proposed for efficient sampling.Together with the improved Levenberg-Marquardt optimization method,the proposed adaptive deep learning method shows great potential in improving solution accuracy.Numerical tests on the elliptic problems without interface conditions,on one elliptic interface problem,and on the convection-dominated problems demonstrate the effectiveness of the proposed method,as it reduces the relative errors by a factor varying from 102 to 104 for different cases.
基金supported by the U.S. DOE Office of Science-Basic Energy Sciences, under Contract No. DE-AC02-06CH11357The research was also supported by the Canadian Light Source and its funding partners. Data for demonstrations were collected at beamlines 25-ID, 20-BM, and 10-ID (MRCAT) of the Advanced Photon Source+1 种基金The NMC-111 electrodes were supplied by the U.S. Department of Energy’s (DOE) CAMP (Cell Analysis, Modeling and Prototyping) Facility, Argonne National LaboratoryThe CAMP Facility is fully supported by the DOE Vehicle Technologies Office (VTO).
文摘X-ray absorption near edge structure(XANES)spectroscopy is a powerful technique for characterizing the chemical state andsymmetry of individual elements within materials,but requires collecting data at many energy points which can be time-consuming.While adaptive sampling methods exist for efficiently collecting spectroscopic data,they often lack domain-specific knowledge about the structure of XANES spectra.Here we demonstrate a knowledge-injected Bayesian optimization approach for adaptive XANES data collection that incorporates understanding of spectral features like absorption edges and pre-edge peaks.We show this method accurately reconstructs the absorption edge of XANES spectra using only 15–20%of the measurement points typically needed for conventional sampling,while maintaining the ability to determine the x-ray energy of the sharp peak after the absorption edge with errors less than 0.03 eV,the absorption edge with errors less than 0.1 eV;and overall root-mean-square errors less than 0.005 compared to traditionally sampled spectra.Our experiments on battery materials and catalysts demonstrate the method’s effectiveness for both static and dynamic XANES measurements,improving data collection efficiency and enabling better time resolution for tracking chemical changes.This approach advances the degree of automation in XANES experiments,reducing the common errors of under-or over-sampling points near the absorption edge and enabling dynamic experiments that require high temporal resolution or limited measurement time.
基金funding support of this research by the National Natural Science Foundation of China(11871443)Shandong Provincial Qingchuang Science and Technology Project(2019KJI002)the Ocean University of China for providing the startup funding(201712011)that is used in supporting this work.
文摘.A non-intrusive reduced order model(ROM)that combines a proper orthogonal decomposition(POD)and an artificial neural network(ANN)is primarily studied to investigate the applicability of the proposed ROM in recovering the solutions with shocks and strong gradients accurately and resolving fine-scale structures efficiently for hyperbolic conservation laws.Its accuracy is demonstrated by solving a high-dimensional parametrized ODE and the one-dimensional viscous Burgers’equation with a parameterized diffusion coefficient.The two-dimensional singlemode Rayleigh-Taylor instability(RTI),where the amplitude of the small perturbation and time are considered as free parameters,is also simulated.An adaptive sampling method in time during the linear regime of the RTI is designed to reduce the number of snapshots required for POD and the training of ANN.The extensive numerical results show that the ROM can achieve an acceptable accuracy with improved efficiency in comparison with the standard full order method.
文摘Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelihood function of the Bayesian method is commonly computationally expensive or analytically unavailable.In this study,in order to circumvent this intractable likelihood function,the approximate Bayesian computation(ABC)is expanded to the IHCPs.In ABC,the high dimensional observations in the intractable likelihood function are equalized by their low dimensional summary statistics.Thus,the performance of the ABC depends on the selection of summary statistics.In this study,a machine learning-based ABC(ML-ABC)is proposed to address the complicated selections of the summary statistics.The Auto-Encoder(AE)is a powerful Machine Learning(ML)framework which can compress the observations into very low dimensional summary statistics with little information loss.In addition,in order to accelerate the calculation of the proposed framework,another neural network(NN)is utilized to construct the mapping between the unknowns and the summary statistics.With this mapping,given arbitrary unknowns,the summary statistics can be obtained efficiently without solving the time-consuming forward problem with numerical method.Furthermore,an adaptive nested sampling method(ANSM)is developed to further improve the efficiency of sampling.The performance of the proposed method is demonstrated with two IHCP cases.
