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Register a new userDatabase optimization for empirical interatomic potential models
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Weighted least squares fitting to a database of quantum mechanical calculations can determine the optimal parameters of empirical potential models. While algorithms exist to provide optimal potential parameters for a given fitting database of structures and their structure property functions, and to estimate prediction errors using Bayesian sampling, defining an optimal fitting database based on potential predictions remains elusive. A testing set of structures and their structure property functions provides an empirical measure of potential transferability. Here, we propose an objective function for fitting databases based on testing set errors. The objective function allows the optimization of the weights in a fitting database, the assessment of the inclusion or removal of structures in the fitting database, or the comparison of two different fitting databases. To showcase this technique, we consider an example Lennard-Jones potential for Ti, where modeling multiple complicated crystal structures is difficult for a radial pair potential. The algorithm finds different optimal fitting databases, depending on the objective function of potential prediction error for a testing set.
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We introduce a Gaussian approximation potential (GAP) for atomistic simulations of liquid and amorphous elemental carbon. Based on a machine-learning representation of the density-functional theory (DFT) potential-energy surface, such interatomic potentials enable materials simulations with close-to DFT accuracy but at much lower computational cost. We first determine the maximum accuracy that any finite-range potential can achieve in carbon structures; then, using a novel hierarchical set of two-, three-, and many-body structural descriptors, we construct a GAP model that can indeed reach the target accuracy. The potential yields accurate energetic and structural properties over a wide range of densities; it also correctly captures the structure of the liquid phases, at variance with state-of-the-art empirical potentials. Exemplary applications of the GAP model to surfaces of diamond-like tetrahedral amorphous carbon (ta-C) are presented, including an estimate of the amorphous materials surface energy, and simulations of high-temperature surface reconstructions (graphitization). The new interatomic potential appears to be promising for realistic and accurate simulations of nanoscale amorphous carbon structures.
Accuracy of molecular dynamics simulations depends crucially on the interatomic potential used to generate forces. The gold standard would be first-principles quantum mechanics (QM) calculations, but these become prohibitively expensive at large simulation scales. Machine learning (ML) based potentials aim for faithful emulation of QM at drastically reduced computational cost. The accuracy and robustness of an ML potential is primarily limited by the quality and diversity of the training dataset. Using the principles of active learning (AL), we present a highly automated approach to dataset construction. The strategy is to use the ML potential under development to sample new atomic configurations and, whenever a configuration is reached for which the ML uncertainty is sufficiently large, collect new QM data. Here, we seek to push the limits of automation, removing as much expert knowledge from the AL process as possible. All sampling is performed using MD simulations starting from an initially disordered configuration, and undergoing non-equilibrium dynamics as driven by time-varying applied temperatures. We demonstrate this approach by building an ML potential for aluminum (ANI-Al). After many AL iterations, ANI-Al teaches itself to predict properties like the radial distribution function in melt, liquid-solid coexistence curve, and crystal properties such as defect energies and barriers. To demonstrate transferability, we perform a 1.3M atom shock simulation, and show that ANI-Al predictions agree very well with DFT calculations on local atomic environments sampled from the nonequilibrium dynamics. Interestingly, the configurations appearing in shock appear to have been well sampled in the AL training dataset, in a way that we illustrate visually.
GeTe is a prototypical phase change material of high interest for applications in optical and electronic non-volatile memories. We present an interatomic potential for the bulk phases of GeTe, which is created using a neural network (NN) representation of the potential-energy surface obtained from reference calculations based on density functional theory. It is demonstrated that the NN potential provides a close to ab initio quality description of a number of properties of liquid, crystalline and amorphous GeTe. The availability of a reliable classical potential allows addressing a number of issues of interest for the technological applications of phase change materials, which are presently beyond the capability of first principles molecular dynamics simulations.
Molecular dynamics (MD) simulation of dislocation migration requires semi-empirical potentials of the interatomic interaction. While there are many reliable semi-empirical potentials for the bcc Fe, the number of the available potentials for the fcc is very limited. In the present study we tested three EAM potentials for the fcc Fe (ABCH97 [Phil. Mag. A, 75, 713-732 (1997)], BCT13 [MSMSE 21, 085004 (2013)] and ZFS18 [J. Comp. Chem. 39, 2420-2431 (2018)]) from literature. It was found that the ABCH97 potential does not provide that the fcc phase is the most stable at any temperature. On the other hand, the fcc phase is always more stable than the bcc phase for the BCT13, ZFS18 potentials. The hcp phase is the most stable phase for the BCT13 potential at any temperature. In order to fix these problems we developed two new EAM potentials (MB1 and MB2). The fcc phase is still more stable than the bcc phase for the MB1 potential but the MB2 potential provides that the bcc phase is the most stable phase from the upper fcc-bcc transformation temperature, T_gamma-delta, to the melting temperature, Tm, and the fcc phase is the most stable phase below T_gamma-delta. This potential also leads to an excellent agreement with the experimental data on the fcc elastic constants and reasonable stacking fault energy which makes it the best potential for the simulation of the dislocation migration in the fcc Fe among all semi-empirical potentials considered in the present study. The MD simulation demonstrated that only the ZFS18, MB1 and MB2 potentials are actually suitable for the simulation of the dislocation migration in the fcc Fe. They lead to the same orders of magnitude for the dislocation velocities and all of them show that the edge dislocation is faster than the screw dislocation. However, the actual values of the dislocation velocities do depend on the employed semi-empirical potential.
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