The interpretation of representations and generalization powers has been a long-standing challenge in the fields of machine learning(ML)and artificial intelligence.This study contributes to understanding the emergence...The interpretation of representations and generalization powers has been a long-standing challenge in the fields of machine learning(ML)and artificial intelligence.This study contributes to understanding the emergence of universal scaling laws in quantum-probabilistic ML.We consider the generative tensor network(GTN)in the form of a matrix-product state as an example and show that with an untrained GTN(such as a random TN state),the negative logarithmic likelihood(NLL)L generally increases linearly with the number of features M,that is,L≃kM+const.This is a consequence of the so-called“catastrophe of orthogonality,”which states that quantum many-body states tend to become exponentially orthogonal to each other as M increases.This study reveals that,while gaining information through training,the linear-scaling law is suppressed by a negative quadratic correction,leading to L≃βM−αM^(2)+const.The scaling coefficients exhibit logarithmic relationships with the number of training samples and quantum channelsχ.The emergence of a quadratic correction term in the NLL for the testing(training)set can be regarded as evidence of the generalization(representation)power of the GTN.Over-parameterization can be identified by the deviation in the values ofαbetween the training and testing sets while increasingχ.We further investigate how orthogonality in the quantum-feature map relates to the satisfaction of quantum-probabilistic interpretation and the representation and generalization powers of the GTN.Unveiling universal scaling laws in quantum-probabilistic ML would be a valuable step toward establishing a white-box ML scheme interpreted within the quantum-probabilistic framework.展开更多
This paper studies the generalization capability of feedforward neural networks (FNN).The mechanism of FNNs for classification is investigated from the geometric and probabilistic viewpoints. It is pointed out that th...This paper studies the generalization capability of feedforward neural networks (FNN).The mechanism of FNNs for classification is investigated from the geometric and probabilistic viewpoints. It is pointed out that the outputs of the output layer in the FNNs for classification correspond to the estimates of posteriori probability of the input pattern samples with desired outputs 1 or 0. The theorem for the generalized kernel function in the radial basis function networks (RBFN) is given. For an 2-layer perceptron network (2-LPN). an idea of using extended samples to improve generalization capability is proposed. Finally. the experimental results of radar target classification are given to verify the generaliztion capability of the RBFNs.展开更多
Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically hav...Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically have rather limited onboard energy on one hand,and require additional flying energy consumption on the other hand.This renders energy-efficient UAV communication with smart energy expenditure of paramount importance.In this paper,via extensive flight experiments,we aim to firstly validate the recently derived theoretical energy model for rotary-wing UAVs,and then develop a general model for those complicated flight scenarios where rigorous theoretical model derivation is quite challenging,if not impossible.Specifically,we first investigate how UAV power consumption varies with its flying speed for the simplest straight-and-level flight.With about 12,000 valid power-speed data points collected,we first apply the model-based curve fitting to obtain the modelling parameters based on the theoretical closed-form energy model in the existing literature.In addition,in order to exclude the potential bias caused by the theoretical energy model,the obtained measurement data is also trained using a model-free deep neural network.It is found that the obtained curve from both methods can match quite well with the theoretical energy model.Next,we further extend the study to arbitrary 2-dimensional(2-D)flight,where,to our best knowledge,no rigorous theoretical derivation is available for the closed-form energy model as a function of its flying speed,direction,and acceleration.To fill the gap,we first propose a heuristic energy model for these more complicated cases,and then provide experimental validation based on the measurement results for circular level flight.展开更多
Changes of word meanings in English are often achieved by the processes of generalization/specialization and pejoration/amelioration.By generalization or specialization,the literal meanings of a word are broadened or ...Changes of word meanings in English are often achieved by the processes of generalization/specialization and pejoration/amelioration.By generalization or specialization,the literal meanings of a word are broadened or narrowed.While by pejoration or amelioration,the associations of a word go downhill or rise.Trough supplying certain examples,a brief picture about meaning changes of words in English is drawn.展开更多
The analysis of an overlaid map with different attributes has a very important function in GIS. In an overlaid map, approximately half of the constructed polygons are tiny and only account for less than 5% of the tota...The analysis of an overlaid map with different attributes has a very important function in GIS. In an overlaid map, approximately half of the constructed polygons are tiny and only account for less than 5% of the total area. In subsequent analysis of an overlaid map, a tiny polygon may require the same amount of computing time and memory space as any large one. In addition, in most cases it is meaningless to treat such polygons as distinct analysis units. So eliminating the tiny polygons is useful to improve efficiency. Now we often use the methods of “boundary comparison” and “fuzzy discriminance” to merge tiny polygons. But in the boundary comparison method, a polygon may be merged into a neighbor of quite different attribute values. In the second method, when the fuzzy grades of two boundary lines are almost the same and their lengths are different, this can lead to large error. In this paper, the partition principle of fuzzy Voronoi (F V) is proposed based on the characteristic of fuzzy boundary and the contiguity of Voronoi diagram. The bigger tiny polygons are divided by Voronoi diagram, and then are merged to neighbor polygon according to contiguity. The F V principle and arithmetic are presented in detail. In the end, an experiment is given; the result has proved that error in the F V method, compared with the two other methods, is only about 30%.展开更多
A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of ...A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.展开更多
Generalization is widely accepted as adaptive behavioral conditions that allow individuals to quickly respond to similar circumstances.But once overgeneralization occurs,e.g.due to the inability to suppress generalize...Generalization is widely accepted as adaptive behavioral conditions that allow individuals to quickly respond to similar circumstances.But once overgeneralization occurs,e.g.due to the inability to suppress generalized fear,it could result in anxiety,depression and related mental disorders.Endocannabinoids(eCB)are important endogenous substance,known to play a role in contextual fear memory generalization.However,less is known in terms of the precise neural mechanism and the regulation of overgeneralization,in particular,for the eCB/CB1R signaling.Using fear memory generalization task,we show that type 1 cannabinoid receptors(CB1R)in hippocampal GABAergic neurons are necessary and sufficient for avoiding overgeneralization.Suppression or deletion of CB1R in hippocampal GABAergic neurons produces overgeneralized contextual fear memory.展开更多
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
In practice, it is necessary to implement an incremental and active learning for a learning method. In terms of such implementation, this paper shows that the previously discussed S-L projection learning is inappropri...In practice, it is necessary to implement an incremental and active learning for a learning method. In terms of such implementation, this paper shows that the previously discussed S-L projection learning is inappropriate to constructing a family of projection learning, and proposes a new version called partial oblique projection (POP) learning. In POP learning, a function space is decomposed into two complementary subspaces, so that functions belonging to one of the subspaces can be completely estimated in noiseless case; while in noisy case, the dispersions are set to be the smallest. In addition, a general form of POP learning is presented and the results of a simulation are given.展开更多
Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the g...Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the great potential to deal with pore pressure prediction.However,most of the traditional deep learning models are less efficient to address generalization problems.To fill this technical gap,in this work,we developed a new adaptive physics-informed deep learning model with high generalization capability to predict pore pressure values directly from seismic data.Specifically,the new model,named CGP-NN,consists of a novel parametric features extraction approach(1DCPP),a stacked multilayer gated recurrent model(multilayer GRU),and an adaptive physics-informed loss function.Through machine training,the developed model can automatically select the optimal physical model to constrain the results for each pore pressure prediction.The CGP-NN model has the best generalization when the physicsrelated metricλ=0.5.A hybrid approach combining Eaton and Bowers methods is also proposed to build machine-learnable labels for solving the problem of few labels.To validate the developed model and methodology,a case study on a complex reservoir in Tarim Basin was further performed to demonstrate the high accuracy on the pore pressure prediction of new wells along with the strong generalization ability.The adaptive physics-informed deep learning approach presented here has potential application in the prediction of pore pressures coupled with multiple genesis mechanisms using seismic data.展开更多
Advancements are reported in computer-generated holography proofing RGB 4K display through a new strategy based on diffraction model-driven deep networks. In the new 4K-DMDNet, the network is not a “black box” anymo...Advancements are reported in computer-generated holography proofing RGB 4K display through a new strategy based on diffraction model-driven deep networks. In the new 4K-DMDNet, the network is not a “black box” anymore. Rather, the input-output relation must obey to the physics of wavefront propagation, which is embedded here as a constraint. Thus, a labelled dataset is not required, and the model shows superior generalization capabilities with respect to data-driven approaches. The method is promising for the new generation of RGB 4K holographic display, as well as augmented and virtual reality systems.展开更多
Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft ...Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft unsteady aerodynamic design and flight dynamics analysis.In this paper,aiming at the problems of poor generalization of traditional aerodynamic models and intelligent models,an intelligent aerodynamic modeling method based on gated neural units is proposed.The time memory characteristics of the gated neural unit is fully utilized,thus the nonlinear flow field characterization ability of the learning and training process is enhanced,and the generalization ability of the whole prediction model is improved.The prediction and verification of the model are carried out under the maneuvering flight condition of NACA0015 airfoil.The results show that the model has good adaptability.In the interpolation prediction,the maximum prediction error of the lift and drag coefficients and the moment coefficient does not exceed 10%,which can basically represent the variation characteristics of the entire flow field.In the construction of extrapolation models,the training model based on the strong nonlinear data has good accuracy for weak nonlinear prediction.Furthermore,the error is larger,even exceeding 20%,which indicates that the extrapolation and generalization capabilities need to be further optimized by integrating physical models.Compared with the conventional state space equation model,the proposed method can improve the extrapolation accuracy and efficiency by 78%and 60%,respectively,which demonstrates the applied potential of this method in aerodynamic modeling.展开更多
In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constrain...In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.展开更多
We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first e...We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.展开更多
Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE(Gravity Recovery and Climate Experiment)Follow-On-like missions and gravitational wave detectors.For such accu...Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE(Gravity Recovery and Climate Experiment)Follow-On-like missions and gravitational wave detectors.For such accuracy of modern space missions,a precise relativistic model of light propagation is required.With the post-Newtonian approximation,we utilize the Synge world function method to study the light propagation in the Earth’s gravitational field,deriving the gravitational delays up to order c^(−4).Then,we investigate the influences of gravitational delays in three inter-satellite laser ranging techniques,including one-way ranging,dual one-way ranging,and transponder-based ranging.By combining the parameters of Kepler orbit,the gravitational delays are expanded up to the order of e^(2)(e is the orbital eccentricity).Finally,considering the GRACE Follow-On-like missions,we estimate the gravitational delays to the level of picometer.The results demonstrate some high-order gravitational and coupling effects,such as c^(−4)-order gravitational delays and coupling of Shapiro and beat frequency,which may be non-negligible for higher precision laser ranging in the future.展开更多
Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existi...Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.展开更多
In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreov...In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreover,we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0.Finally,we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.展开更多
将粒子群优化(PSO)算法与BP神经网络相结合,应用在传感器静态非线性特性的校正中.用PSO算法所得到的全局最优值作为BP神经网络的初始权值,训练BP神经网络,训练结束后的神经网络作为传感器的静态特性校正器.应用结果表明,该方法可以提高B...将粒子群优化(PSO)算法与BP神经网络相结合,应用在传感器静态非线性特性的校正中.用PSO算法所得到的全局最优值作为BP神经网络的初始权值,训练BP神经网络,训练结束后的神经网络作为传感器的静态特性校正器.应用结果表明,该方法可以提高BP神经网络的精度,并且该神经网络具有良好的泛化能力.
Abstract：
A static nonlinear errors method for correcting the sensors based on BP neural network using particle swarm optimization (PSO) is described. The global best values of particle swarm are used as initial weights of BP neural network to train BP neural network. Then the trained neural network is regarded as the sensor's corrector. The application results show that this method can improve the precision of the BP neural network, and the generalization capability of the neural network is good.展开更多
提出了一种基于最小二乘支持向量机的织物剪切性能预测模型,并且采用遗传算法进行最小二乘支持向量机的参数优化,将获得的样本进行归一化处理后,将其输入预测模型以得到预测结果.仿真结果表明,基于最小二乘支持向量机的预测模型比BP神...提出了一种基于最小二乘支持向量机的织物剪切性能预测模型,并且采用遗传算法进行最小二乘支持向量机的参数优化,将获得的样本进行归一化处理后,将其输入预测模型以得到预测结果.仿真结果表明,基于最小二乘支持向量机的预测模型比BP神经网络和线性回归方法具有更高的精度和范化能力.
Abstract：
A new method is proposed to predict the fabric shearing property with least square support vector machines ( LS-SVM ). The genetic algorithm is investigated to select the parameters of LS-SVM models as a means of improving the LS- SVM prediction. After normalizing the sampling data, the sampling data are inputted into the model to gain the prediction result. The simulation results show the prediction model gives better forecasting accuracy and generalization ability than BP neural network and linear regression method.展开更多
基金supported in part by the Beijing Natural Science Foundation (Grant No. 1232025)the Ministry of Education Key Laboratory of Quantum Physics and Photonic Quantum Information (Grant No. ZYGX2024K020)Academy for Multidisciplinary Studies, Capital Normal University.
文摘The interpretation of representations and generalization powers has been a long-standing challenge in the fields of machine learning(ML)and artificial intelligence.This study contributes to understanding the emergence of universal scaling laws in quantum-probabilistic ML.We consider the generative tensor network(GTN)in the form of a matrix-product state as an example and show that with an untrained GTN(such as a random TN state),the negative logarithmic likelihood(NLL)L generally increases linearly with the number of features M,that is,L≃kM+const.This is a consequence of the so-called“catastrophe of orthogonality,”which states that quantum many-body states tend to become exponentially orthogonal to each other as M increases.This study reveals that,while gaining information through training,the linear-scaling law is suppressed by a negative quadratic correction,leading to L≃βM−αM^(2)+const.The scaling coefficients exhibit logarithmic relationships with the number of training samples and quantum channelsχ.The emergence of a quadratic correction term in the NLL for the testing(training)set can be regarded as evidence of the generalization(representation)power of the GTN.Over-parameterization can be identified by the deviation in the values ofαbetween the training and testing sets while increasingχ.We further investigate how orthogonality in the quantum-feature map relates to the satisfaction of quantum-probabilistic interpretation and the representation and generalization powers of the GTN.Unveiling universal scaling laws in quantum-probabilistic ML would be a valuable step toward establishing a white-box ML scheme interpreted within the quantum-probabilistic framework.
文摘This paper studies the generalization capability of feedforward neural networks (FNN).The mechanism of FNNs for classification is investigated from the geometric and probabilistic viewpoints. It is pointed out that the outputs of the output layer in the FNNs for classification correspond to the estimates of posteriori probability of the input pattern samples with desired outputs 1 or 0. The theorem for the generalized kernel function in the radial basis function networks (RBFN) is given. For an 2-layer perceptron network (2-LPN). an idea of using extended samples to improve generalization capability is proposed. Finally. the experimental results of radar target classification are given to verify the generaliztion capability of the RBFNs.
基金This work was supported in part by the Program for Innovative Talents and Entrepreneur in Jiangsu Province under Grant 1104000402in part by the Research Fund by Nanjing Government under Grant 1104000396+4 种基金in part by the National Science Foundation of China under Grants 62001109&61921004in part by the China Postdoctoral Science Foundation under Grants BX20200083&2020M681456in part by the Fundamental Research Funds for the Central Universities of China under Grants 3204002004A2&2242020R20011in part by the open research fund of the National and Local Joint Engineering Laboratory of RF Integration and Micro-Assembly Technology under Grant No.KFJJ20180205in part by the NUPTSF Grants No.NY218113&No.NY219077.
文摘Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically have rather limited onboard energy on one hand,and require additional flying energy consumption on the other hand.This renders energy-efficient UAV communication with smart energy expenditure of paramount importance.In this paper,via extensive flight experiments,we aim to firstly validate the recently derived theoretical energy model for rotary-wing UAVs,and then develop a general model for those complicated flight scenarios where rigorous theoretical model derivation is quite challenging,if not impossible.Specifically,we first investigate how UAV power consumption varies with its flying speed for the simplest straight-and-level flight.With about 12,000 valid power-speed data points collected,we first apply the model-based curve fitting to obtain the modelling parameters based on the theoretical closed-form energy model in the existing literature.In addition,in order to exclude the potential bias caused by the theoretical energy model,the obtained measurement data is also trained using a model-free deep neural network.It is found that the obtained curve from both methods can match quite well with the theoretical energy model.Next,we further extend the study to arbitrary 2-dimensional(2-D)flight,where,to our best knowledge,no rigorous theoretical derivation is available for the closed-form energy model as a function of its flying speed,direction,and acceleration.To fill the gap,we first propose a heuristic energy model for these more complicated cases,and then provide experimental validation based on the measurement results for circular level flight.
文摘Changes of word meanings in English are often achieved by the processes of generalization/specialization and pejoration/amelioration.By generalization or specialization,the literal meanings of a word are broadened or narrowed.While by pejoration or amelioration,the associations of a word go downhill or rise.Trough supplying certain examples,a brief picture about meaning changes of words in English is drawn.
基金Supported by the National Natural Science Foundation of China(No.6983 3 0 10 )
文摘The analysis of an overlaid map with different attributes has a very important function in GIS. In an overlaid map, approximately half of the constructed polygons are tiny and only account for less than 5% of the total area. In subsequent analysis of an overlaid map, a tiny polygon may require the same amount of computing time and memory space as any large one. In addition, in most cases it is meaningless to treat such polygons as distinct analysis units. So eliminating the tiny polygons is useful to improve efficiency. Now we often use the methods of “boundary comparison” and “fuzzy discriminance” to merge tiny polygons. But in the boundary comparison method, a polygon may be merged into a neighbor of quite different attribute values. In the second method, when the fuzzy grades of two boundary lines are almost the same and their lengths are different, this can lead to large error. In this paper, the partition principle of fuzzy Voronoi (F V) is proposed based on the characteristic of fuzzy boundary and the contiguity of Voronoi diagram. The bigger tiny polygons are divided by Voronoi diagram, and then are merged to neighbor polygon according to contiguity. The F V principle and arithmetic are presented in detail. In the end, an experiment is given; the result has proved that error in the F V method, compared with the two other methods, is only about 30%.
基金The Project Supported by National Natural Science Foundation of China.
文摘A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.
文摘Generalization is widely accepted as adaptive behavioral conditions that allow individuals to quickly respond to similar circumstances.But once overgeneralization occurs,e.g.due to the inability to suppress generalized fear,it could result in anxiety,depression and related mental disorders.Endocannabinoids(eCB)are important endogenous substance,known to play a role in contextual fear memory generalization.However,less is known in terms of the precise neural mechanism and the regulation of overgeneralization,in particular,for the eCB/CB1R signaling.Using fear memory generalization task,we show that type 1 cannabinoid receptors(CB1R)in hippocampal GABAergic neurons are necessary and sufficient for avoiding overgeneralization.Suppression or deletion of CB1R in hippocampal GABAergic neurons produces overgeneralized contextual fear memory.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
文摘In practice, it is necessary to implement an incremental and active learning for a learning method. In terms of such implementation, this paper shows that the previously discussed S-L projection learning is inappropriate to constructing a family of projection learning, and proposes a new version called partial oblique projection (POP) learning. In POP learning, a function space is decomposed into two complementary subspaces, so that functions belonging to one of the subspaces can be completely estimated in noiseless case; while in noisy case, the dispersions are set to be the smallest. In addition, a general form of POP learning is presented and the results of a simulation are given.
基金funded by the National Natural Science Foundation of China(General Program:No.52074314,No.U19B6003-05)National Key Research and Development Program of China(2019YFA0708303-05)。
文摘Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the great potential to deal with pore pressure prediction.However,most of the traditional deep learning models are less efficient to address generalization problems.To fill this technical gap,in this work,we developed a new adaptive physics-informed deep learning model with high generalization capability to predict pore pressure values directly from seismic data.Specifically,the new model,named CGP-NN,consists of a novel parametric features extraction approach(1DCPP),a stacked multilayer gated recurrent model(multilayer GRU),and an adaptive physics-informed loss function.Through machine training,the developed model can automatically select the optimal physical model to constrain the results for each pore pressure prediction.The CGP-NN model has the best generalization when the physicsrelated metricλ=0.5.A hybrid approach combining Eaton and Bowers methods is also proposed to build machine-learnable labels for solving the problem of few labels.To validate the developed model and methodology,a case study on a complex reservoir in Tarim Basin was further performed to demonstrate the high accuracy on the pore pressure prediction of new wells along with the strong generalization ability.The adaptive physics-informed deep learning approach presented here has potential application in the prediction of pore pressures coupled with multiple genesis mechanisms using seismic data.
文摘Advancements are reported in computer-generated holography proofing RGB 4K display through a new strategy based on diffraction model-driven deep networks. In the new 4K-DMDNet, the network is not a “black box” anymore. Rather, the input-output relation must obey to the physics of wavefront propagation, which is embedded here as a constraint. Thus, a labelled dataset is not required, and the model shows superior generalization capabilities with respect to data-driven approaches. The method is promising for the new generation of RGB 4K holographic display, as well as augmented and virtual reality systems.
基金supported in part by the National Natural Science Foundation of China (No. 12202363)。
文摘Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft unsteady aerodynamic design and flight dynamics analysis.In this paper,aiming at the problems of poor generalization of traditional aerodynamic models and intelligent models,an intelligent aerodynamic modeling method based on gated neural units is proposed.The time memory characteristics of the gated neural unit is fully utilized,thus the nonlinear flow field characterization ability of the learning and training process is enhanced,and the generalization ability of the whole prediction model is improved.The prediction and verification of the model are carried out under the maneuvering flight condition of NACA0015 airfoil.The results show that the model has good adaptability.In the interpolation prediction,the maximum prediction error of the lift and drag coefficients and the moment coefficient does not exceed 10%,which can basically represent the variation characteristics of the entire flow field.In the construction of extrapolation models,the training model based on the strong nonlinear data has good accuracy for weak nonlinear prediction.Furthermore,the error is larger,even exceeding 20%,which indicates that the extrapolation and generalization capabilities need to be further optimized by integrating physical models.Compared with the conventional state space equation model,the proposed method can improve the extrapolation accuracy and efficiency by 78%and 60%,respectively,which demonstrates the applied potential of this method in aerodynamic modeling.
基金supported by the NSFC(12271184)the Guangzhou Basic and Applied Basic Research Foundation(2024A04J10001).
文摘In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.
文摘We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12247150,12305062,12175076,and 11925503)the Post-doctoral Science Foundation of China(Grant No.2022M721257)the Guangdong Major Project of Basic and Applied Basic Research(Grant No.2019B030302001).
文摘Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE(Gravity Recovery and Climate Experiment)Follow-On-like missions and gravitational wave detectors.For such accuracy of modern space missions,a precise relativistic model of light propagation is required.With the post-Newtonian approximation,we utilize the Synge world function method to study the light propagation in the Earth’s gravitational field,deriving the gravitational delays up to order c^(−4).Then,we investigate the influences of gravitational delays in three inter-satellite laser ranging techniques,including one-way ranging,dual one-way ranging,and transponder-based ranging.By combining the parameters of Kepler orbit,the gravitational delays are expanded up to the order of e^(2)(e is the orbital eccentricity).Finally,considering the GRACE Follow-On-like missions,we estimate the gravitational delays to the level of picometer.The results demonstrate some high-order gravitational and coupling effects,such as c^(−4)-order gravitational delays and coupling of Shapiro and beat frequency,which may be non-negligible for higher precision laser ranging in the future.
基金supported by the National Natural Science Foundation of China(61833005)the Humanities and Social Science Fund of Ministry of Education of China(23YJAZH031)+1 种基金the Natural Science Foundation of Hebei Province of China(A2023209002,A2019209005)the Tangshan Science and Technology Bureau Program of Hebei Province of China(19130222g)。
文摘Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.
基金Supported by National Natural Science Foundation of China(Grant No.11271141).
文摘In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreover,we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0.Finally,we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.
文摘将粒子群优化(PSO)算法与BP神经网络相结合,应用在传感器静态非线性特性的校正中.用PSO算法所得到的全局最优值作为BP神经网络的初始权值,训练BP神经网络,训练结束后的神经网络作为传感器的静态特性校正器.应用结果表明,该方法可以提高BP神经网络的精度,并且该神经网络具有良好的泛化能力.
Abstract：
A static nonlinear errors method for correcting the sensors based on BP neural network using particle swarm optimization (PSO) is described. The global best values of particle swarm are used as initial weights of BP neural network to train BP neural network. Then the trained neural network is regarded as the sensor's corrector. The application results show that this method can improve the precision of the BP neural network, and the generalization capability of the neural network is good.
文摘提出了一种基于最小二乘支持向量机的织物剪切性能预测模型,并且采用遗传算法进行最小二乘支持向量机的参数优化,将获得的样本进行归一化处理后,将其输入预测模型以得到预测结果.仿真结果表明,基于最小二乘支持向量机的预测模型比BP神经网络和线性回归方法具有更高的精度和范化能力.
Abstract：
A new method is proposed to predict the fabric shearing property with least square support vector machines ( LS-SVM ). The genetic algorithm is investigated to select the parameters of LS-SVM models as a means of improving the LS- SVM prediction. After normalizing the sampling data, the sampling data are inputted into the model to gain the prediction result. The simulation results show the prediction model gives better forecasting accuracy and generalization ability than BP neural network and linear regression method.
