Solution Of Multi-electron Systems Using Variational Quantum Monte Carlo Method Based On Neural Network

Theoretical calculation of multi-electron systems is an important subject in physics.In recent years,with the rapid development of artificial intelligence related research,Deep Learning,Neural Networks and other technologies have played an important role in many fields of natural science research.Recently,David Pfau from Deep Mind Technologies and his collaborators proposed the Fermi neural network(Ferminet,[Phys.Rev.R2,033429(2020)])to achieve accurate fitting of the wave function of the Fermion system.With the help of the variational method,the solving process of physical problems is changed into the optimization process of neural network.Then the Fermi neural network can output the wave function of the system.In this thesis,we study how to use neural networks to study physical system.Subsequently,we improve the Ferminet with the Transformer structure containing the self-attention mechanism(the improved network is named Transform-Ferminet,denoted as TFN),and use the TFN to compute small molecule systems.In the first chapter of this thesis,we first introduce the background of the solution of multi-electron systems and the related basis of neural network.And then we introduce the recent progress of the research on the combination of neural network and physical system.In the second chapter,we introduce the structure and the optimization process of the Ferminet in detail.Then,the ground state energies of four molecules,LiH,NH₃,CH₃NH₂and C₂H₅OH,were calculated according to the number of electrons from less to more.The optimization process and the output results of the Ferminet were analyzed.In the third chapter,we introduce the Transformer structure containing the self-attention mechanism,which has been widely used in deep learning research recently.In order to improve the expressive ability of the Ferminet,we use the Transformer structure to replace the single linear connection structure.In this thesis,three different Transformer structures are added in the first layer of the single electron stream,the hidden layer of the single and double electron stream of the Ferminet respectively,and the physical considerations of adding these three structures are analyzed.Then,the effects of the number of parameters of the self-attention mechanism and the number of hidden units of linear connection structure in Transformer on the expression ability of the network are analyzed by calculating the methane's ground state energy.Compared with the linear connection structure,the self-attention mechanism is more expressive and uses fewer trainable parameters.In the fourth chapter,the ground state energy is calculated with the TFN and the original Ferminet as a example.The energy optimization process and ground state energy from the two methods are compared.and we analyzed the hidden layer parameters of the two methods.The results show that the expressive ability of TFN is similar to that of the original Ferminet after the optimization process tends to be stable.In particular,the TFN can reduce the amonut of network parameters which shows that the TFN can decrease the number of parameters without loss of accuracy.