Development And Optimization Of A Neural Network Potential-based Atomic Kinetics Monte Carlo Program

The nuclear reactor pressure vessel is one of the most important components in a nuclear power plant and its service life plays a decisive role in the safe operation of the entire nuclear power plant.As a classical Fe-Cu binary alloy,the nuclear reactor pressure vessel is subject to irradiation damage during service,which accelerates the aging process by precipitation of solute atoms.Therefore,atomic-level microscopic simulations are needed to understand the internal microscopic evolution of the material,and numerical computer simulations can help materials researchers to study these physicochemical phenomena in depth.Kinetic Monte Carlo methods are commonly used in scientific calculations today,allowing long time and large scale numerical simulations,and are an effective means to perform multi-scale physical simulations.Meanwhile,with the continuous development of artificial intelligence technology,many researchers have developed neural network potentials with higher accuracy than traditional empirical potentials using neural networks.For this reason,a kinetic Monte Carlo procedure combining neural network potentials will be better for materials simulation.In this paper,the following work is done for the atomic kinetic Monte Carlo simulation procedure based on neural network potentials:(1)To combine atomic kinetic Monte Carlo methods with neural network potentials for calculations,atomic fingerprinting algorithms are needed to calculate atomic fingerprints as inputs to the neural network.Conventional atomic fingerprinting algorithms usually take into account only the distance of the interactions between atoms and do not take into account the directionality of the interactions.Here we derive the formula for calculating the angular interaction between atoms from the conventional embedded atomic potential,introduce it into the conventional atomic fingerprinting algorithm,and reduce it to a single-loop summation,so that the new atomic fingerprinting algorithm can be effectively combined with the previous triple encoding algorithm.At the same time,in order to consider the time complexity of the calculation,a method is proposed to make the whole atomic fingerprint calculation simpler by using a multiple-degree simplification.(2)A neural network potential for Fe-Cu binary alloys was developed,and the accuracy of this neural network potential was tested.The required Fe-Cu binary alloy dataset was first calculated using the first-principles computing software VASP,and the dataset was trained using the open-source program Tensor Alloy.Three different activation functions,Re LU,Soft Plus and Square Plus,were used to ensure the accuracy of the neural network potential and to compare the effect of gradient-smooth and non-smooth activation functions on fitting a high-dimensional complex potential surface.atomic angle-directed action was also included in the calculation.The results of the trained neural network potential are compared with the first principles,and the results show that the computational error of the neural network potential is smaller,and the accuracy of the neural network potential is improved after using the gradient-smooth activation function and adding the atomic angular direction calculation.(3)The developed Fe-Cu binary alloy neural network potential was tested in an atomic kinetic Monte Carlo program using a long time simulation.The hot spot function of the program was also analyzed and it was found that the atomic fingerprint and the forward computation time share of the neural network increased significantly at higher vacancy concentrations.The test results showed that the number of isolated Cu atoms was significantly decreased using the calculation with angular momentum m=1 when observing the number of isolated Cu atoms,verifying the accuracy of the angular direction calculation.The simulation time of the program increases significantly for both the increase in the simulation scale of the vacancy concentration and also for the higher angular momentum of the calculated atoms in the angular direction.