Machine Learning Potential Method And Its Application In The Structure Predictions And Phase Transition Simulations

Studying the structure and phase transition of materials from the atomic level is important for guiding the material synthesis and understanding the material evolution inside planets.Although there already exists a lot of exciting discoveries in the research of structure and phase transition of materials experimentally,there are still some difficulties under extreme conditions.Currently,theoretical simulation as a powerful tool can assist experiments and even guide experimental synthesis.It is necessary to determine the interaction model between atoms or molecules for structure prediction and phase transition simulation.Density functional theory(DFT)as an ab initio method has the high accuracy and transferability.Currently structure prediction and molecular dynamics simulation driven by DFT have led to many exciting discoveries,such as the transparent dense sodium.Due to the unfavorable scaling of computational cost,DFT-based simulation is restricted to systems containing a few hundreds of atoms.In the phase transition simulation,using the small simulation box will force the phase transitions to occur in a concerted manner with all atoms moving collectively in the entire simulation box instead of nucleation and growth.This may result in artificial stability of the structures,so in order to observe the phase transition within accessible simulation time,it is necessary to set the pressure far beyond the thermodynamic transition pressure.However,this may prevent transitions to some phases and hide information about the kinetics.On the other hand,empirical potentials can be used in the structure prediction and molecular dynamics simulation with large systems.However,for some systems,empirical potentials will lead to unreliable structure search results,wrong transition paths and mechanisms due to their lower accuracy and transferability.In order to overcome the above limitations,we developed the machine learning potential(MLP)based on the Gaussian process regression,and applied it to the structure prediction as well as reconstructive soild-soild phase transition,and achieved the following innovative scientific research results:1.We developed the machine learning potential named CALYPSO-GAP by combining Gaussian process regression and modified atom-centered symmetry functions.To test the validity and precision of MLP in the fitting potential energy surface,we constructed a data set consisting of 15,624 boron clusters using DFT and randomly chose 3571 clusters as testing set,in which the lower root mean square error of MLP means higher precision.Then,for testing the transferability of MLP and its performance on structure optimization,we generated 257 boron clusters randomly using CALYPSO and performed structure relaxation using MLP(interfaced with conjugate gradient method)and VASP respectively.We compared the distribution of bond length and energy of these relaxed structures,which show that MLP has higher transferability for extrapolative structures and similar ability to perform structure optimization comparing with VASP.In the framework of Gaussian process regression,we defined the variance of predicted value of energy to measure its reliability and numerical test showed that this definition is very effective.2.In order to accelerate structure prediction of CALYPSO by MLP,we proposed two schemes.In the first scheme,DFT or empirical potential calculation in the CALYPSO is substituted by well-trained MLP.Firstly,we performed a benchmark test of structure search using B36 and B40 clusters and the results showed that CALYPSO structure search accelerated by MLP can reproduce these two structures easily.Then we performed structure prediction of boron crystal under ambient pressure and found a series of metastable structures,among which a cubic structure is named c-B24.It not only appears unusual four-center-two-electron bonds but also has superconducting and superhard properties.Obviously,the quality of MLP plays an important role in the reliability of structure prediction results of scheme one,i.e.,the construction of data set.If we know very little about the systems we want to predict,the structure search would fail.To overcome this difficulty,we proposed the second scheme,named adaptive structure prediction,which can start with a small and random data set and then enlarge data set while refining MLP during structure search.The advantage of this scheme is that it can use the smallest data set to ensure the accuracy and transferability of MLP.We used structure search of B84 cluster as an example to test this scheme.Currently,the structural type of B84 cluster is still controversial.Our developed scheme successfully reproduced the quasi-planar structure proposed by Rahane et al.and found a new core-shell and cage-like structures.These results approve that core-shell structure is the ground state structure type of B84 cluster.By estimating the number of self-consistent calculations of DFT required in the prediction process,the computational cost can be reduced by-2 orders of magnitude in scheme two.3.Understanding the transition path and mechanism of reconstructive phase transition is crucial for guiding material synthesis and understanding planet internal structure.However,molecular dynamics simulation based on DFT is restricted to the phase transition barrier and the size of simulation box.In the simulation,it is difficult to observe phase transition,even though a phase transition can be observed but will lose a lot of information in detail.To overcome this difficulty,we developed the method that combine the metadynamics with MLP to simulate reconstructive solid-solid phase transition.The utility of the method was demonstrated by the phase transition of gallium nitride(GaN)from wurtzite(B4)to rocksalt(B1)phases under high pressure.Firstly,we constructed a data set containing five well-designed structural types and from which we obtained a MLP.By comparing the enthalpy under different pressure,radial distribution function and elastic properties,MLP was proved to have high precision and transferability.By comparing the computational time of MLP with DFT and empirical potentials,it shows that MLP has high computational efficiency.Secondly,we applied the MLP to simulate the pressure induced B4-B1 phase transition using a 64 atoms simulation box under hydrostatic and uniaxial stress as a benchmark test.The simulated transition path was consistent with the first-principles metadynamics simulation.Finally,we extended the size of simulation box to 4096 atoms and external pressure to general stress conditions including hydrostatic,uniaxial,and shear stress.The simulation reveals the transition path with excellent quality.Microscopic events that are critical to reconstructive phase transition but not possible with small-scale DFT simulation,such as nucleation center formation and growth,and their responses to changing stress conditions,are clearly reproduced in our simulation.These results prove that metadynamics simulation combined with MLP is a powerful tool for studying the reconstructive solid-solid phase transition.