This study investigates photonuclear reaction(γ,n)cross-sections using Bayesian neural network(BNN)analysis.After determining the optimal network architecture,which features two hidden layers,each with 50 hidden node...This study investigates photonuclear reaction(γ,n)cross-sections using Bayesian neural network(BNN)analysis.After determining the optimal network architecture,which features two hidden layers,each with 50 hidden nodes,training was conducted for 30,000 iterations to ensure comprehensive data capture.By analyzing the distribution of absolute errors positively correlated with the cross-section for the isotope 159Tb,as well as the relative errors unrelated to the cross-section,we confirmed that the network effectively captured the data features without overfitting.Comparison with the TENDL-2021 Database demonstrated the BNN's reliability in fitting photonuclear cross-sections with lower average errors.The predictions for nuclei with single and double giant dipole resonance peak cross-sections,the accurate determination of the photoneutron reaction threshold in the low-energy region,and the precise description of trends in the high-energy cross-sections further demonstrate the network's generalization ability on the validation set.This can be attributed to the consistency of the training data.By using consistent training sets from different laboratories,Bayesian neural networks can predict nearby unknown cross-sections based on existing laboratory data,thereby estimating the potential differences between other laboratories'existing data and their own measurement results.Experimental measurements of photonuclear reactions on the newly constructed SLEGS beamline will contribute to clarifying the differences in cross-sections within the existing data.展开更多
A machine learning approach based on Bayesian neural networks was developed to predict the complete fusion cross-sections of weakly bound nuclei.This method was trained and validated using 475 experimental data points...A machine learning approach based on Bayesian neural networks was developed to predict the complete fusion cross-sections of weakly bound nuclei.This method was trained and validated using 475 experimental data points from 39 reaction systems induced by ^(6,7)Li,^(9)Be,and ^(10)B.The constructed Bayesian neural network demonstrated a high degree of accuracy in evaluating complete fusion cross-sections.By comparing the predicted cross-sections with those obtained from a single-barrier penetration model,the suppression effect of ^(6,7)Li and ^(9)Be with a stable nucleus was systematically analyzed.In the cases of ^(6)Li and ^(7)Li,less suppression was predicted for relatively light-mass targets than for heavy-mass targets,and a notably distinct dependence relationship was identified,suggesting that the predominant breakup mechanisms might change in different mass target regions.In addition,minimum suppression factors were predicted to occur near target nuclei with neutron-closed shell.展开更多
Accurate identification of unknown internal parameters in photovoltaic(PV)cells is crucial and significantly affects the subsequent system-performance analysis and control.However,noise,insufficient data acquisition,a...Accurate identification of unknown internal parameters in photovoltaic(PV)cells is crucial and significantly affects the subsequent system-performance analysis and control.However,noise,insufficient data acquisition,and loss of recorded data can deteriorate the extraction accuracy of unknown parameters.Hence,this study proposes an intelligent parameter-identification strategy that integrates artificial ecosystem optimization(AEO)and a Bayesian neural network(BNN)for PV cell parameter extraction.A BNN is used for data preprocessing,including data denoising and prediction.Furthermore,the AEO algorithm is utilized to identify unknown parameters in the single-diode model(SDM),double-diode model(DDM),and three-diode model(TDM).Nine other metaheuristic algorithms(MhAs)are adopted for an unbiased and comprehensive validation.Simulation results show that BNN-based data preprocessing com-bined with effective MhAs significantly improve the parameter-extraction accuracy and stability compared with methods without data preprocessing.For instance,under denoised data,the accuracies of the SDM,DDM,and TDM increase by 99.69%,99.70%,and 99.69%,respectively,whereas their accuracy improvements increase by 66.71%,59.65%,and 70.36%,respectively.展开更多
Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian ne...Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network （PBNN） nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.展开更多
This work is an attempt to improve the Bayesian neural network (BNN) for studying photoneutron yield cross sections as a function of the charge number Z, mass number A, and incident energy ε. The BNN was improved in ...This work is an attempt to improve the Bayesian neural network (BNN) for studying photoneutron yield cross sections as a function of the charge number Z, mass number A, and incident energy ε. The BNN was improved in terms of three aspects:numerical parameters, input layer, and network structure. First, by minimizing the deviations between the predictions and data, the numerical parameters, including the hidden layer number, hidden node number, and activation function, were selected. It was found that the BNN with three hidden layers, 10 hidden nodes, and sigmoid activation function provided the smallest deviations. Second, based on known knowledge,such as the isospin dependence and shape effect, the optimal ground-state properties were selected as input neurons. Third, the Lorentzian function was applied to map the hidden nodes to the output cross sections, and the empirical formula of the Lorentzian parameters was applied to link some of the input nodes to the output cross sections. It was found that the last two aspects improved the predictions and avoided overfitting, especially for the axially deformed nucleus.展开更多
High entropy alloys(HEAs)have excellent application prospects in catalysis because of their rich components and configuration space.In this work,we develop a Bayesian neural network(BNN)based on energies calculated wi...High entropy alloys(HEAs)have excellent application prospects in catalysis because of their rich components and configuration space.In this work,we develop a Bayesian neural network(BNN)based on energies calculated with density functional theory to search the configuration space of the CoNiRhRu HEA system.The BNN model was developed by considering six independent features of Co-Ni,Co-Rh,CoRu,Ni-Rh,Ni-Ru,and Rh-Ru in different shells and energies of structures as the labels.The root mean squared error of the energy predicted by BNN is 1.37 me V/atom.Moreover,the influence of feature periodicity on the energy of HEA in theoretical calculations is discussed.We found that when the neural network is optimized to a certain extent,only using the accuracy indicator of root mean square error to evaluate model performance is no longer accurate in some scenarios.More importantly,we reveal the importance of uncertainty quantification for neural networks to predict new structures of HEAs with proper confidence based on BNN.展开更多
Deuteron separation energy is not only the basis for validating the nuclear mass models and nucleon-nucleon interaction potential,but also can determine the stability of a nuclide to certain extent.Bayesian neural net...Deuteron separation energy is not only the basis for validating the nuclear mass models and nucleon-nucleon interaction potential,but also can determine the stability of a nuclide to certain extent.Bayesian neural network(BNN)approach,which has strong predictive power and can naturally give theoretical errors of predicted values,had been successfully applied to study the different kinds of separations except the deuteron separation.In this paper,several typical nuclear mass models,such as macroscopic model BW2,macroscopic-microscopic model WS4,and microscopic model HFB-31,are chosen to study the deuteron separation energy combining BNN approach.The root-mean-square deviations of these models are partly reduced.In addition,the inclusion of physical parameters related to the pair and shell effects in the input layer can further improve the theoretical accuracy for the deuteron separation energy.The results show that the theoretical predictions are more reliable as more physical features of BNN approach are included.展开更多
Creating new molecules with desired properties is a fundamental and challenging problem in chemistry. Reinforcement learning (RL) has shown its utility in this area where the target chemical property values can serve ...Creating new molecules with desired properties is a fundamental and challenging problem in chemistry. Reinforcement learning (RL) has shown its utility in this area where the target chemical property values can serve as a reward signal. At each step of making a new molecule, the RL agent learns selecting an action from a list of many chemically valid actions for a given molecule, implying a great uncertainty associated with its learning. In a traditional implementation of deep RL algorithms, deterministic neural networks are typically employed, thus allowing the agent to choose one action from one sampled action at each step. In this paper, we proposed a new strategy of applying Bayesian neural networks to RL to reduce uncertainty so that the agent can choose one action from a pool of sampled actions at each step, and investigated its benefits in molecule design. Our experiments suggested the Bayesian approach could create molecules of desirable chemical quality while maintained their diversity, a very difficult goal to achieve in machine learning of molecules. We further exploited their diversity by using them to train a generative model to yield more novel drug-like molecules, which were absent in the training molecules as we know novelty is essential for drug candidate molecules. In conclusion, Bayesian approach could offer a balance between exploitation and exploration in RL, and a balance between optimization and diversity in molecule design.展开更多
The effective and timely diagnosis and treatment of ocular diseases are key to the rapid recovery of patients.Today,the mass disease that needs attention in this context is cataracts.Although deep learning has signifi...The effective and timely diagnosis and treatment of ocular diseases are key to the rapid recovery of patients.Today,the mass disease that needs attention in this context is cataracts.Although deep learning has significantly advanced the analysis of ocular disease images,there is a need for a probabilistic model to generate the distributions of potential outcomes and thusmake decisions related to uncertainty quantification.Therefore,this study implements a Bayesian Convolutional Neural Networks(BCNN)model for predicting cataracts by assigning probability values to the predictions.It prepares convolutional neural network(CNN)and BCNN models.The proposed BCNN model is CNN-based in which reparameterization is in the first and last layers of the CNN model.This study then trains them on a dataset of cataract images filtered from the ocular disease fundus images fromKaggle.The deep CNN model has an accuracy of 95%,while the BCNN model has an accuracy of 93.75% along with information on uncertainty estimation of cataracts and normal eye conditions.When compared with other methods,the proposed work reveals that it can be a promising solution for cataract prediction with uncertainty estimation.展开更多
The Bayesian neural network(BNN)has been widely used to study nuclear physics in recent years.In this study,a BNN was applied to optimize seven theoretical nuclear mass models,namely,six global models and one local mo...The Bayesian neural network(BNN)has been widely used to study nuclear physics in recent years.In this study,a BNN was applied to optimize seven theoretical nuclear mass models,namely,six global models and one local model.The accuracy of these models in describing and predicting masses of nuclei with both the proton number and the neutron number greater than or equal to eight was improved effectively for two types of numerical experiments,particularly for the liquid drop model and the relativistic mean-field theory,whose root mean square deviations(RMSDs)for describing(predicting)nuclear masses were reduced by 81.5%-90.6%(66.9%-84.2%).Additionally,the relatively stable RMSDs as nuclei move away from theβ-stability line and the good agreement with experimental single-neutron separation energies further confirm the reliability of the BNN.展开更多
This study utilizes the Bayesian neural network(BNN)method in machine learning to learn and predict the cross-sectional data of ^(28)Si projectile fragmentation for different targets at different energies and to quant...This study utilizes the Bayesian neural network(BNN)method in machine learning to learn and predict the cross-sectional data of ^(28)Si projectile fragmentation for different targets at different energies and to quantify the uncertainty.The detailed modeling process of the BNN is presented,and its prediction results are compared with those of the Cummings,Nilsen,EPAX2,EPAX3,and FRACS models and experimental measurement values.The results reveal that,compared with other models,the BNN method achieves the smallest root-mean-square error(RMSE)and the highest agreement with the experimental values.Only the BNN method and FRACS model show a significant odd-even staggering effect;however,the results of the BNN method are closer to the experimental values.Furthermore,the BNN method is the only model capable of reproducing data features with low cross-section values at Z=9,and the average ratio of the predicted to experimental values of the BNN is close to 1.0.These results indicate that the BNN method can accurately reproduce and predict the fragment production cross sections of ^(28)Si projectile fragmentation and demonstrate its ability to capture key data characteristics.展开更多
Nuclear level density(NLD)is a critical parameter for understanding nuclear reactions and the structure of atomic nuclei;however,accurate estimation of NLD is challenging owing to limitations inherent in both experime...Nuclear level density(NLD)is a critical parameter for understanding nuclear reactions and the structure of atomic nuclei;however,accurate estimation of NLD is challenging owing to limitations inherent in both experimental measurements and theoretical models.This paper presents a sophisticated approach using Bayesian neural networks(BNNs)to analyze NLD across a wide range of models.It uniquely incorporates the assessment of model uncertainties.The application of BNNs demonstrates remarkable success in accurately predicting NLD values when compared to recent experimental data,confirming the effectiveness of our methodology.The reliability and predictive power of the BNN approach not only validates its current application but also encourages its integration into future analyses of nuclear reaction cross sections.展开更多
Machine learning models are constructed to predict fragment production cross sections in projectile fragmentation(PF)reactions using Bayesian neural network(BNN)techniques.The massive learning for BNN models is based ...Machine learning models are constructed to predict fragment production cross sections in projectile fragmentation(PF)reactions using Bayesian neural network(BNN)techniques.The massive learning for BNN models is based on 6393 fragments from 53 measured projectile fragmentation reactions.A direct BNN model and physical guiding BNN via FRACS parametrization(BNN+FRACS)model have been constructed to predict the fragment cross section in projectile fragmentation reactions.It is verified that the BNN and BNN+FRACS models can reproduce a wide range of fragment productions in PF reactions with incident energies from 40 MeV/u to 1 GeV/u,reaction systems with projectile nuclei from^40 Ar to^208 Pb,and various target nuclei.The high precision of the BNN and BNN+FRACS models makes them applicable for the low production rate of extremely rare isotopes in future PF reactions with large projectile nucleus asymmetry in the new generation of radioactive nuclear beam factories.展开更多
The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei.The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large r...The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei.The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square(rms)deviations from data,i.e.,0.949μN and 1.272μN for odd-neutron nuclei and odd-proton nuclei,respectively.By including the dependence of the nuclear spin and Schmidt magnetic moment,the machine-learning approach precisely describes the magnetic moments of odd-A uclei with rms deviations of 0.036μN for odd-neutron nuclei and 0.061μN for odd-proton nuclei.Furthermore,the evolution of magnetic moments along isotopic chains,including the staggering and sudden jump trend,which are difficult to describe using nuclear models,have been well reproduced by the Bayesian neural network(BNN)approach.The magnetic moments of doubly closed-shell±1 nuclei,for example,isoscalar and isovector magnetic moments,have been well studied and compared with the corresponding non-relativistic and relativistic calculations.展开更多
Accurate wind speed and consequently wind power forecasts form a critical enabling tool for large scale wind energy adoption.Probabilistic machine learning models such as Bayesian Neural Network(BNN)models are often p...Accurate wind speed and consequently wind power forecasts form a critical enabling tool for large scale wind energy adoption.Probabilistic machine learning models such as Bayesian Neural Network(BNN)models are often preferred in the forecasting task as they facilitate estimates of predictive uncertainty and automatic relevance determination(ARD).Hybrid Monte Carlo(HMC)is widely used to perform asymptotically exact inference of the network parameters.A significant limitation to the increased adoption of HMC in inference for large scale machine learning systems is the exponential degradation of the acceptance rates and the corresponding effective sample sizes with increasing model dimensionality due to numerical integration errors.This paper presents a solution to this problem by sampling from a modified or shadow Hamiltonian that is conserved to a higher-order by the leapfrog integrator.BNNs trained using Separable Shadow Hamiltonian Hybrid Monte Carlo(S2HMC)are used to forecast one hour ahead wind speeds on the Wind Atlas for South Africa(WASA)datasets.Experimental results find that S2HMC yields higher effective sample sizes than the competing HMC.The predictive performance of S2HMC and HMC based BNNs is found to be similar.We further perform hierarchical inference for BNN parameters by combining the S2HMC sampler with Gibbs sampling of hyperparameters for relevance determination.A generalisable ARD committee framework is introduced to synthesise the various sampler ARD outputs into robust feature selections.Experimental results show that this ARD committee approach selects features of high predictive information value.Further,the results show that dimensionality reduction performed through this approach improves the sampling performance of samplers that suffer from random walk behaviour such as Metropolis–Hastings(MH).展开更多
The Monte-Carlo samples of pion, kaon and proton generated from 0.3 GeV/c to 1.2 GeV/c by the ‘tester＇ generator from SIMBES which are used to simulate the detector of BES Ⅱ are identified with the Bayesian neural ...The Monte-Carlo samples of pion, kaon and proton generated from 0.3 GeV/c to 1.2 GeV/c by the ‘tester＇ generator from SIMBES which are used to simulate the detector of BES Ⅱ are identified with the Bayesian neural networks （BNN）. The pion identification and misidentification efficiencies are obviously better at high momentum region using BNN than the methods of χ^2 analysis of dE/dX and TOF information. The kaon identification and misidentification efficiencies are obviously better from 0.3 GeV/c to 1.2 GeV/c using BNN than the methods of X2 analysis. The proton identification and misidentification efficiencies using BNN are basically consistent with the ones of χ^2 analysis. The anti-proton identification and misidentification efficiencies are better below 0.6 GeV/c using BNN than the methods of χ^2 analysis.展开更多
Bayesian regularized BP neural network（BRBPNN） technique was applied in the chlorophyll-α prediction of Nanzui water area in Dongting Lake. Through BP network interpolation method, the input and output samples of t...Bayesian regularized BP neural network（BRBPNN） technique was applied in the chlorophyll-α prediction of Nanzui water area in Dongting Lake. Through BP network interpolation method, the input and output samples of the network were obtained. After the selection of input variables using stepwise/multiple linear regression method in SPSS i1.0 software, the BRBPNN model was established between chlorophyll-α and environmental parameters, biological parameters. The achieved optimal network structure was 3-11-1 with the correlation coefficients and the mean square errors for the training set and the test set as 0.999 and 0.000？8426, 0.981 and 0.0216 respectively. The sum of square weights between each input neuron and the hidden layer of optimal BRBPNN models of different structures indicated that the effect of individual input parameter on chlorophyll- α declined in the order of alga amount 〉 secchi disc depth（SD） 〉 electrical conductivity （EC）. Additionally, it also demonstrated that the contributions of these three factors were the maximal for the change of chlorophyll-α concentration, total phosphorus（TP） and total nitrogen（TN） were the minimal. All the results showed that BRBPNN model was capable of automated regularization parameter selection and thus it may ensure the excellent generation ability and robustness. Thus, this study laid the foundation for the application of BRBPNN model in the analysis of aquatic ecological data（chlorophyll-α prediction） and the explanation about the effective eutrophication treatment measures for Nanzui water area in Dongting Lake.展开更多
A neural network with a feed forward topology and Bayesian regularization training algorithm is used to predict the austenite formation temperatures （At1 and A13） by considering the percentage of alloying elements i...A neural network with a feed forward topology and Bayesian regularization training algorithm is used to predict the austenite formation temperatures （At1 and A13） by considering the percentage of alloying elements in chemical composition of steel. The data base used here involves a large variety of different steel types such as struc- tural steels, stainless steels, rail steels, spring steels, high temperature creep resisting steels and tool steels. Scatter diagrams and mean relative error （MRE） statistical criteria are used to compare the performance of developed neural network with the results of Andrew% empirical equations and a feed forward neural network with ＂gradient descent with momentum＂ training algorithm. The results showed that Bayesian regularization neural network has the best performance. Also, due to the satisfactory results of the developed neural network, it was used to investigate the effect of the chemical composition on Ac1 and At3 temperatures. Results are in accordance with materials science theories.展开更多
Enterprise Information System management has become an increasingly vital factor for many firms. Several organizations have encountered problems when attempting to evaluate organizational performance. Measurement of p...Enterprise Information System management has become an increasingly vital factor for many firms. Several organizations have encountered problems when attempting to evaluate organizational performance. Measurement of performance metrics is a key challenge for a huge number of firms. In order to preserve relevance and adaptability in competitive markets, it has become essential to respond proactively to complex events through informed decision-making that is supported by technology. Therefore, the objective of this study was to apply neural networks to the modeling, simulation, and forecasting of the effects of the performance indicators of Enterprise Information Systems on the achievement of corporate objectives and value creation. A set of quantifiable and sizeable conditionally independent associations were derived using a simplified joint probability distribution technique. Bayesian Neural Networks were utilized to describe the link between random variables (features) and to concisely and easily specify the joint probability distribution. The research demonstrated that Bayesian networks could effectively explore complex logical linkages by employing probability to represent uncertainty and probabilistic rules;and by applying impact models from Bayesian taxonomies to achieve learning and reasoning processes.展开更多
基金supported by National key research and development program(No.2022YFA1602404)the National Natural Science Foundation of China(Nos.12388102,12275338,12005280)the Key Laboratory of Nuclear Data foundation(No.JCKY2022201C152)。
文摘This study investigates photonuclear reaction(γ,n)cross-sections using Bayesian neural network(BNN)analysis.After determining the optimal network architecture,which features two hidden layers,each with 50 hidden nodes,training was conducted for 30,000 iterations to ensure comprehensive data capture.By analyzing the distribution of absolute errors positively correlated with the cross-section for the isotope 159Tb,as well as the relative errors unrelated to the cross-section,we confirmed that the network effectively captured the data features without overfitting.Comparison with the TENDL-2021 Database demonstrated the BNN's reliability in fitting photonuclear cross-sections with lower average errors.The predictions for nuclei with single and double giant dipole resonance peak cross-sections,the accurate determination of the photoneutron reaction threshold in the low-energy region,and the precise description of trends in the high-energy cross-sections further demonstrate the network's generalization ability on the validation set.This can be attributed to the consistency of the training data.By using consistent training sets from different laboratories,Bayesian neural networks can predict nearby unknown cross-sections based on existing laboratory data,thereby estimating the potential differences between other laboratories'existing data and their own measurement results.Experimental measurements of photonuclear reactions on the newly constructed SLEGS beamline will contribute to clarifying the differences in cross-sections within the existing data.
基金supported by National Natural Science Foundation of China(Nos.12105080 and 12375123)China Postdoctoral Science Foundation(No.2023M731015)Natural Science Foundation of Henan Province(No.242300422048).
文摘A machine learning approach based on Bayesian neural networks was developed to predict the complete fusion cross-sections of weakly bound nuclei.This method was trained and validated using 475 experimental data points from 39 reaction systems induced by ^(6,7)Li,^(9)Be,and ^(10)B.The constructed Bayesian neural network demonstrated a high degree of accuracy in evaluating complete fusion cross-sections.By comparing the predicted cross-sections with those obtained from a single-barrier penetration model,the suppression effect of ^(6,7)Li and ^(9)Be with a stable nucleus was systematically analyzed.In the cases of ^(6)Li and ^(7)Li,less suppression was predicted for relatively light-mass targets than for heavy-mass targets,and a notably distinct dependence relationship was identified,suggesting that the predominant breakup mechanisms might change in different mass target regions.In addition,minimum suppression factors were predicted to occur near target nuclei with neutron-closed shell.
基金supported by the National Natural Science Foundation of China(62263014)the Yunnan Provincial Basic Research Project(202301AT070443,202401AT070344).
文摘Accurate identification of unknown internal parameters in photovoltaic(PV)cells is crucial and significantly affects the subsequent system-performance analysis and control.However,noise,insufficient data acquisition,and loss of recorded data can deteriorate the extraction accuracy of unknown parameters.Hence,this study proposes an intelligent parameter-identification strategy that integrates artificial ecosystem optimization(AEO)and a Bayesian neural network(BNN)for PV cell parameter extraction.A BNN is used for data preprocessing,including data denoising and prediction.Furthermore,the AEO algorithm is utilized to identify unknown parameters in the single-diode model(SDM),double-diode model(DDM),and three-diode model(TDM).Nine other metaheuristic algorithms(MhAs)are adopted for an unbiased and comprehensive validation.Simulation results show that BNN-based data preprocessing com-bined with effective MhAs significantly improve the parameter-extraction accuracy and stability compared with methods without data preprocessing.For instance,under denoised data,the accuracies of the SDM,DDM,and TDM increase by 99.69%,99.70%,and 99.69%,respectively,whereas their accuracy improvements increase by 66.71%,59.65%,and 70.36%,respectively.
基金supported by the National Natural Science Foundation of China(Grant No.41374118)the Research Fund for the Higher Education Doctoral Program of China(Grant No.20120162110015)+3 种基金the China Postdoctoral Science Foundation(Grant No.2015M580700)the Hunan Provincial Natural Science Foundation,the China(Grant No.2016JJ3086)the Hunan Provincial Science and Technology Program,China(Grant No.2015JC3067)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant No.15B138)
文摘Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network （PBNN） nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.
基金supported by the National Natural Science Foundation of China(Nos.11905018 and 11875328).
文摘This work is an attempt to improve the Bayesian neural network (BNN) for studying photoneutron yield cross sections as a function of the charge number Z, mass number A, and incident energy ε. The BNN was improved in terms of three aspects:numerical parameters, input layer, and network structure. First, by minimizing the deviations between the predictions and data, the numerical parameters, including the hidden layer number, hidden node number, and activation function, were selected. It was found that the BNN with three hidden layers, 10 hidden nodes, and sigmoid activation function provided the smallest deviations. Second, based on known knowledge,such as the isospin dependence and shape effect, the optimal ground-state properties were selected as input neurons. Third, the Lorentzian function was applied to map the hidden nodes to the output cross sections, and the empirical formula of the Lorentzian parameters was applied to link some of the input nodes to the output cross sections. It was found that the last two aspects improved the predictions and avoided overfitting, especially for the axially deformed nucleus.
基金supported by the Shanghai Rising-Star Program (20QA1406800)the National Natural Science Foundation of China (22072091,91745102,92045301)。
文摘High entropy alloys(HEAs)have excellent application prospects in catalysis because of their rich components and configuration space.In this work,we develop a Bayesian neural network(BNN)based on energies calculated with density functional theory to search the configuration space of the CoNiRhRu HEA system.The BNN model was developed by considering six independent features of Co-Ni,Co-Rh,CoRu,Ni-Rh,Ni-Ru,and Rh-Ru in different shells and energies of structures as the labels.The root mean squared error of the energy predicted by BNN is 1.37 me V/atom.Moreover,the influence of feature periodicity on the energy of HEA in theoretical calculations is discussed.We found that when the neural network is optimized to a certain extent,only using the accuracy indicator of root mean square error to evaluate model performance is no longer accurate in some scenarios.More importantly,we reveal the importance of uncertainty quantification for neural networks to predict new structures of HEAs with proper confidence based on BNN.
基金Supported by National Natural Science Foundation of China (12065003)Central Government Guidance Funds for Local Scientific and Technological Development of China (Guike ZY22096024)+1 种基金Natural Science Foundation of Guangxi (2019GXNSFDA185011)Scientific Research and Technology Development Project of Guilin (20210104-2)。
文摘Deuteron separation energy is not only the basis for validating the nuclear mass models and nucleon-nucleon interaction potential,but also can determine the stability of a nuclide to certain extent.Bayesian neural network(BNN)approach,which has strong predictive power and can naturally give theoretical errors of predicted values,had been successfully applied to study the different kinds of separations except the deuteron separation.In this paper,several typical nuclear mass models,such as macroscopic model BW2,macroscopic-microscopic model WS4,and microscopic model HFB-31,are chosen to study the deuteron separation energy combining BNN approach.The root-mean-square deviations of these models are partly reduced.In addition,the inclusion of physical parameters related to the pair and shell effects in the input layer can further improve the theoretical accuracy for the deuteron separation energy.The results show that the theoretical predictions are more reliable as more physical features of BNN approach are included.
文摘Creating new molecules with desired properties is a fundamental and challenging problem in chemistry. Reinforcement learning (RL) has shown its utility in this area where the target chemical property values can serve as a reward signal. At each step of making a new molecule, the RL agent learns selecting an action from a list of many chemically valid actions for a given molecule, implying a great uncertainty associated with its learning. In a traditional implementation of deep RL algorithms, deterministic neural networks are typically employed, thus allowing the agent to choose one action from one sampled action at each step. In this paper, we proposed a new strategy of applying Bayesian neural networks to RL to reduce uncertainty so that the agent can choose one action from a pool of sampled actions at each step, and investigated its benefits in molecule design. Our experiments suggested the Bayesian approach could create molecules of desirable chemical quality while maintained their diversity, a very difficult goal to achieve in machine learning of molecules. We further exploited their diversity by using them to train a generative model to yield more novel drug-like molecules, which were absent in the training molecules as we know novelty is essential for drug candidate molecules. In conclusion, Bayesian approach could offer a balance between exploitation and exploration in RL, and a balance between optimization and diversity in molecule design.
基金Saudi Arabia for funding this work through Small Research Group Project under Grant Number RGP.1/316/45.
文摘The effective and timely diagnosis and treatment of ocular diseases are key to the rapid recovery of patients.Today,the mass disease that needs attention in this context is cataracts.Although deep learning has significantly advanced the analysis of ocular disease images,there is a need for a probabilistic model to generate the distributions of potential outcomes and thusmake decisions related to uncertainty quantification.Therefore,this study implements a Bayesian Convolutional Neural Networks(BCNN)model for predicting cataracts by assigning probability values to the predictions.It prepares convolutional neural network(CNN)and BCNN models.The proposed BCNN model is CNN-based in which reparameterization is in the first and last layers of the CNN model.This study then trains them on a dataset of cataract images filtered from the ocular disease fundus images fromKaggle.The deep CNN model has an accuracy of 95%,while the BCNN model has an accuracy of 93.75% along with information on uncertainty estimation of cataracts and normal eye conditions.When compared with other methods,the proposed work reveals that it can be a promising solution for cataract prediction with uncertainty estimation.
文摘The Bayesian neural network(BNN)has been widely used to study nuclear physics in recent years.In this study,a BNN was applied to optimize seven theoretical nuclear mass models,namely,six global models and one local model.The accuracy of these models in describing and predicting masses of nuclei with both the proton number and the neutron number greater than or equal to eight was improved effectively for two types of numerical experiments,particularly for the liquid drop model and the relativistic mean-field theory,whose root mean square deviations(RMSDs)for describing(predicting)nuclear masses were reduced by 81.5%-90.6%(66.9%-84.2%).Additionally,the relatively stable RMSDs as nuclei move away from theβ-stability line and the good agreement with experimental single-neutron separation energies further confirm the reliability of the BNN.
基金Supported by the National Nature Science Foundation of China(11075100,11347198,11565001)the Natural Science Foundation of Shanxi Province,China(2011011001-2)+1 种基金the Shanxi Provincial Foundation for Returned Overseas Chinese Scholars(2011-058)the Postgraduate Science and Technology Innovation Project of Shanxi Normal University(2023XBY004)。
文摘This study utilizes the Bayesian neural network(BNN)method in machine learning to learn and predict the cross-sectional data of ^(28)Si projectile fragmentation for different targets at different energies and to quantify the uncertainty.The detailed modeling process of the BNN is presented,and its prediction results are compared with those of the Cummings,Nilsen,EPAX2,EPAX3,and FRACS models and experimental measurement values.The results reveal that,compared with other models,the BNN method achieves the smallest root-mean-square error(RMSE)and the highest agreement with the experimental values.Only the BNN method and FRACS model show a significant odd-even staggering effect;however,the results of the BNN method are closer to the experimental values.Furthermore,the BNN method is the only model capable of reproducing data features with low cross-section values at Z=9,and the average ratio of the predicted to experimental values of the BNN is close to 1.0.These results indicate that the BNN method can accurately reproduce and predict the fragment production cross sections of ^(28)Si projectile fragmentation and demonstrate its ability to capture key data characteristics.
基金Supported by the the National Natural Science Foundation of China(12275359,12375129,11875323,11961141003)the National Key R&D Program of China(2023YFA1606402)+2 种基金the Continuous Basic Scientific Research Projectthe Funding of China Institute of Atomic Energy(YZ222407001301,YZ232604001601)the Leading Innovation Project of the CNNC(LC192209000701,LC202309000201)。
文摘Nuclear level density(NLD)is a critical parameter for understanding nuclear reactions and the structure of atomic nuclei;however,accurate estimation of NLD is challenging owing to limitations inherent in both experimental measurements and theoretical models.This paper presents a sophisticated approach using Bayesian neural networks(BNNs)to analyze NLD across a wide range of models.It uniquely incorporates the assessment of model uncertainties.The application of BNNs demonstrates remarkable success in accurately predicting NLD values when compared to recent experimental data,confirming the effectiveness of our methodology.The reliability and predictive power of the BNN approach not only validates its current application but also encourages its integration into future analyses of nuclear reaction cross sections.
基金Supported by the National Natural Science Foundation of China(11975091)the Program for Innovative Research Team(in Science and Technology)in University of Henan Province(21IRTSTHN011),China。
文摘Machine learning models are constructed to predict fragment production cross sections in projectile fragmentation(PF)reactions using Bayesian neural network(BNN)techniques.The massive learning for BNN models is based on 6393 fragments from 53 measured projectile fragmentation reactions.A direct BNN model and physical guiding BNN via FRACS parametrization(BNN+FRACS)model have been constructed to predict the fragment cross section in projectile fragmentation reactions.It is verified that the BNN and BNN+FRACS models can reproduce a wide range of fragment productions in PF reactions with incident energies from 40 MeV/u to 1 GeV/u,reaction systems with projectile nuclei from^40 Ar to^208 Pb,and various target nuclei.The high precision of the BNN and BNN+FRACS models makes them applicable for the low production rate of extremely rare isotopes in future PF reactions with large projectile nucleus asymmetry in the new generation of radioactive nuclear beam factories.
基金Supported by the National Natural Science Foundation of China(11675063,11875070,11205068)the Open fund for Discipline Construction,Institute of Physical Science and Information Technology,Anhui University。
文摘The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei.The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square(rms)deviations from data,i.e.,0.949μN and 1.272μN for odd-neutron nuclei and odd-proton nuclei,respectively.By including the dependence of the nuclear spin and Schmidt magnetic moment,the machine-learning approach precisely describes the magnetic moments of odd-A uclei with rms deviations of 0.036μN for odd-neutron nuclei and 0.061μN for odd-proton nuclei.Furthermore,the evolution of magnetic moments along isotopic chains,including the staggering and sudden jump trend,which are difficult to describe using nuclear models,have been well reproduced by the Bayesian neural network(BNN)approach.The magnetic moments of doubly closed-shell±1 nuclei,for example,isoscalar and isovector magnetic moments,have been well studied and compared with the corresponding non-relativistic and relativistic calculations.
文摘Accurate wind speed and consequently wind power forecasts form a critical enabling tool for large scale wind energy adoption.Probabilistic machine learning models such as Bayesian Neural Network(BNN)models are often preferred in the forecasting task as they facilitate estimates of predictive uncertainty and automatic relevance determination(ARD).Hybrid Monte Carlo(HMC)is widely used to perform asymptotically exact inference of the network parameters.A significant limitation to the increased adoption of HMC in inference for large scale machine learning systems is the exponential degradation of the acceptance rates and the corresponding effective sample sizes with increasing model dimensionality due to numerical integration errors.This paper presents a solution to this problem by sampling from a modified or shadow Hamiltonian that is conserved to a higher-order by the leapfrog integrator.BNNs trained using Separable Shadow Hamiltonian Hybrid Monte Carlo(S2HMC)are used to forecast one hour ahead wind speeds on the Wind Atlas for South Africa(WASA)datasets.Experimental results find that S2HMC yields higher effective sample sizes than the competing HMC.The predictive performance of S2HMC and HMC based BNNs is found to be similar.We further perform hierarchical inference for BNN parameters by combining the S2HMC sampler with Gibbs sampling of hyperparameters for relevance determination.A generalisable ARD committee framework is introduced to synthesise the various sampler ARD outputs into robust feature selections.Experimental results show that this ARD committee approach selects features of high predictive information value.Further,the results show that dimensionality reduction performed through this approach improves the sampling performance of samplers that suffer from random walk behaviour such as Metropolis–Hastings(MH).
基金Supported by National Natural Science Foundation of China(10605014)
文摘The Monte-Carlo samples of pion, kaon and proton generated from 0.3 GeV/c to 1.2 GeV/c by the ‘tester＇ generator from SIMBES which are used to simulate the detector of BES Ⅱ are identified with the Bayesian neural networks （BNN）. The pion identification and misidentification efficiencies are obviously better at high momentum region using BNN than the methods of χ^2 analysis of dE/dX and TOF information. The kaon identification and misidentification efficiencies are obviously better from 0.3 GeV/c to 1.2 GeV/c using BNN than the methods of X2 analysis. The proton identification and misidentification efficiencies using BNN are basically consistent with the ones of χ^2 analysis. The anti-proton identification and misidentification efficiencies are better below 0.6 GeV/c using BNN than the methods of χ^2 analysis.
文摘Bayesian regularized BP neural network（BRBPNN） technique was applied in the chlorophyll-α prediction of Nanzui water area in Dongting Lake. Through BP network interpolation method, the input and output samples of the network were obtained. After the selection of input variables using stepwise/multiple linear regression method in SPSS i1.0 software, the BRBPNN model was established between chlorophyll-α and environmental parameters, biological parameters. The achieved optimal network structure was 3-11-1 with the correlation coefficients and the mean square errors for the training set and the test set as 0.999 and 0.000？8426, 0.981 and 0.0216 respectively. The sum of square weights between each input neuron and the hidden layer of optimal BRBPNN models of different structures indicated that the effect of individual input parameter on chlorophyll- α declined in the order of alga amount 〉 secchi disc depth（SD） 〉 electrical conductivity （EC）. Additionally, it also demonstrated that the contributions of these three factors were the maximal for the change of chlorophyll-α concentration, total phosphorus（TP） and total nitrogen（TN） were the minimal. All the results showed that BRBPNN model was capable of automated regularization parameter selection and thus it may ensure the excellent generation ability and robustness. Thus, this study laid the foundation for the application of BRBPNN model in the analysis of aquatic ecological data（chlorophyll-α prediction） and the explanation about the effective eutrophication treatment measures for Nanzui water area in Dongting Lake.
基金Financial support of mechanical engineering center of excellence at Roudbar Azad University
文摘A neural network with a feed forward topology and Bayesian regularization training algorithm is used to predict the austenite formation temperatures （At1 and A13） by considering the percentage of alloying elements in chemical composition of steel. The data base used here involves a large variety of different steel types such as struc- tural steels, stainless steels, rail steels, spring steels, high temperature creep resisting steels and tool steels. Scatter diagrams and mean relative error （MRE） statistical criteria are used to compare the performance of developed neural network with the results of Andrew% empirical equations and a feed forward neural network with ＂gradient descent with momentum＂ training algorithm. The results showed that Bayesian regularization neural network has the best performance. Also, due to the satisfactory results of the developed neural network, it was used to investigate the effect of the chemical composition on Ac1 and At3 temperatures. Results are in accordance with materials science theories.
文摘Enterprise Information System management has become an increasingly vital factor for many firms. Several organizations have encountered problems when attempting to evaluate organizational performance. Measurement of performance metrics is a key challenge for a huge number of firms. In order to preserve relevance and adaptability in competitive markets, it has become essential to respond proactively to complex events through informed decision-making that is supported by technology. Therefore, the objective of this study was to apply neural networks to the modeling, simulation, and forecasting of the effects of the performance indicators of Enterprise Information Systems on the achievement of corporate objectives and value creation. A set of quantifiable and sizeable conditionally independent associations were derived using a simplified joint probability distribution technique. Bayesian Neural Networks were utilized to describe the link between random variables (features) and to concisely and easily specify the joint probability distribution. The research demonstrated that Bayesian networks could effectively explore complex logical linkages by employing probability to represent uncertainty and probabilistic rules;and by applying impact models from Bayesian taxonomies to achieve learning and reasoning processes.
