The ground state energy curves of one-dimensional ＆function interacting bose and fermi gas are fitted with simple algebraic approximations according to their asymptotic behaviors.
We train a neural network to identify impurities in the experimental images obtained by the scanning tunneling microscope(STM)measurements.The neural network is first trained with a large number of simulated data and ...We train a neural network to identify impurities in the experimental images obtained by the scanning tunneling microscope(STM)measurements.The neural network is first trained with a large number of simulated data and then the trained neural network is applied to identify a set of experimental images taken at different voltages.We use the convolutional neural network to extract features from the images and also implement the attention mechanism to capture the correlations between images taken at different voltages.We note that the simulated data can capture the universal Friedel oscillation but cannot properly describe the non-universal physics short-range physics nearby an impurity,as well as noises in the experimental data.And we emphasize that the key of this approach is to properly deal with these differences between simulated data and experimental data.Here we show that even by including uncorrelated white noises in the simulated data,the performance of the neural network on experimental data can be significantly improved.To prevent the neural network from learning unphysical short-range physics,we also develop another method to evaluate the confidence of the neural network prediction on experimental data and to add this confidence measure into the loss function.We show that adding such an extra loss function can also improve the performance on experimental data.Our research can inspire future similar applications of machine learning on experimental data analysis.展开更多
We prove in theorems 2 and 3 that for ID Bosons with repulsive delta function interaction with any number of components and any Young tableau,the energy per particle as N→∞is the same as for spinless Bosons.
基金Supported by the National Natural Science Foundation of China under Grant No 20081305646.
文摘The ground state energy curves of one-dimensional ＆function interacting bose and fermi gas are fitted with simple algebraic approximations according to their asymptotic behaviors.
基金supported by Beijing Outstanding Scholar Programthe National Key Research and Development Program of China(Grant No. 2016YFA0301600)+3 种基金the National Natural Science Foundation of China(Grant No. 11734010)supported by a startup fund from UCSDsupported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China
文摘We train a neural network to identify impurities in the experimental images obtained by the scanning tunneling microscope(STM)measurements.The neural network is first trained with a large number of simulated data and then the trained neural network is applied to identify a set of experimental images taken at different voltages.We use the convolutional neural network to extract features from the images and also implement the attention mechanism to capture the correlations between images taken at different voltages.We note that the simulated data can capture the universal Friedel oscillation but cannot properly describe the non-universal physics short-range physics nearby an impurity,as well as noises in the experimental data.And we emphasize that the key of this approach is to properly deal with these differences between simulated data and experimental data.Here we show that even by including uncorrelated white noises in the simulated data,the performance of the neural network on experimental data can be significantly improved.To prevent the neural network from learning unphysical short-range physics,we also develop another method to evaluate the confidence of the neural network prediction on experimental data and to add this confidence measure into the loss function.We show that adding such an extra loss function can also improve the performance on experimental data.Our research can inspire future similar applications of machine learning on experimental data analysis.
基金Partly supported by the National Natural Science Foundation of China under Grant Nos 10847002 and J0825002.
文摘We prove in theorems 2 and 3 that for ID Bosons with repulsive delta function interaction with any number of components and any Young tableau,the energy per particle as N→∞is the same as for spinless Bosons.
