Neural Networks For Predicting Electron Transport Properties Of Mesoscopic Systems

In recent years,computation physicists have demonstrated that machine-learning techniques can be used to speed up the simulation of complex systems and can also assist in the study of quantum transport properties.Exploring the influence of disorder on the transport properties requires a lot of calculation time.In order to accelerate the simulation on the transport properties of mesoscopic systems,we train neural networks to predict transport properties of a quasi-one-dimensional tight-binding model with disordered on-site energies.For the Anderson disorder model(modelⅠ),the on-site energies of all sites in the scattering region pick up values randomly and independently from a given interval,it is found that the performance of the neural network depends strongly on the system size.For a small system size,the neural network can predict accurately the conductance at the Fermi energy.With an increase in the system size,the mean absolute error(MAE)increases.This tendency persists under an increase in the number of training samples and the number of neurons in the neural network.The physical mechanism behind this phenomenon can be ascribed to the universal conductance fluctuation and dimension curse.To reduce the effective dimension of features fed into the neural network,we consider the case of substitutional doping model(modelⅡ)where the impurities have a fixed on-site energy,random position distribution,and variable concentration.The results show that even for a relatively large system size,the trained neural network in modelⅡperforms much better in predicting the conductance at the Fermi energy.When the prediction target is changed to the average conductance under a finite bias(average value of 10 conductances at energies near the Fermi energy),the MAE can be reduced by almost a half.The small fluctuation of the average conductance reduces further the prediction difficulty of the neural network.Our work reveals that the accuracy of neural networks in predicting the conductance of disordered mesoscopic transport systems is related to the universal conductance fluctuation and dimension curse.The trained neural network can predict quickly and accurately the disorder-averaged transport properties for model Ⅱ.