We report that single interatomic potential, developed using Gaussian regression of density functional theory calculation data, has high accuracy and flexibility to describe phonon transport with ab initio accuracy in two different atomistic configurations: perfect crystalline Si and crystalline Si with vacancies. The high accuracy of second-and third-order force constants from the Gaussian approximation potential (GAP) are demonstrated with phonon dispersion, Grüneisen parameter, three-phonon scattering rate, phonon-vacancy scattering rate, and thermal conductivity, all of which are very close to the results from density functional theory calculation. We also show that the widely used empirical potentials (Stillinger-Weber and Tersoff) produce much larger errors compared to the GAP. The computational cost of GAP is higher than the two empirical potentials, but five orders of magnitude lower than the density functional theory calculation. Our work shows that GAP can provide a new opportunity for studying phonon transport in partially disordered crystalline phases with the high predictive power of ab initio calculation but at a feasible computational cost.
Many scientific and engineering processes produce spatially unstructured data. However, most data-driven models require a feature matrix that enforces both a set number and order of features for each sample. They thus cannot be easily constructed for an unstructured dataset. Therefore, a graph based data-driven model to perform inference on fields defined on an unstructured mesh, using a graph convolutional neural network (GCNN) is presented. The ability of the method to predict global properties from spatially irregular measurements with high accuracy is demonstrated by predicting the drag force associated with laminar flow around airfoils from scattered velocity measurements. The network can infer from field samples at different resolutions, and is invariant to the order in which the measurements within each sample are presented. The GCNN method, using inductive convolutional layers and adaptive pooling, is able to predict this quantity with a validation R
2 above 0.98, and a Normalized Mean Squared Error below 0.01, without relying on spatial structure.
We discuss the dependence of the propagon contribution to thermal conductivity on the medium range order (MRO) in amorphous silicon. Three different amorphous structures with the same size of 3.28 nm were studied. Among these three structures, two structures were constructed with experimentally observed MRO [Treacy and Borisenko, Science. 335, 6071 (2012)] and the other structure is from continuous random network (CRN), which lacks MRO and thus represents a randomized amorphous structure [Barkema and Mousseau, Physical Review B, 62, 8 (2000)].Using the simulated fluctuation electron microscopy and dihedral angle distribution, we confirm that the first two structures contain MRO in the length scale of 10-20 Å while the CRN structure does not. The transport of propagons in the MRO and CRN structures are compared using the dynamic structural factor calculation and normal mode decomposition of the molecular dynamics simulation data, showing noticeably longer lifetime of propagons in the MRO structures than in the CRN structure. The propagon thermal conductivity in the MRO structures is estimated 50% larger than that in the CRN structure.
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