High-pressure phase ID swaps graph convolution for Gaussian kernels: 20-30 minutes instead of 5-6 hours, accuracy on par with DGCNN

Phase identification no longer needs graph convolution over atomic adjacency; a set of sampled Gaussian densities is enough for an ordinary neural network to decide which phase a local environment belongs to. The strongest prior machine-learning route was the dynamic graph convolutional network used by Erhard et al., which builds each atom's local environment into a graph and classifies it with edge convolution. At environment sizes of 16, 32 and 64 neighbors, the Gaussian kernel model reaches 78%, 86% and 90% test accuracy, against 75%, 85% and 92% for DGCNN, a comparable level.

Each atom is treated as the center of a Gaussian density, and a set of atom detectors fixed around the origin records only the density summed over all atoms at that point. The input follows from a neural tangent kernel argument: summing random Fourier features makes the first-layer weights act as implicit sample points, so the first layer can be skipped and the Gaussian kernel sum computed directly. Detector coordinates and the Gaussian width are optimized during training, and grid initialization and normal sampling around the origin give similar results; models use ReLU activations, the Adam optimizer and cross-entropy loss.

The speedup comes from a simpler computation, a few distance calculations plus a standard neural network. DGCNN requires edge convolution, which is substantially heavier. Compared across models and local environment sizes on the same HPC environment, the Gaussian kernel model generates predictions for a simulation in about 20-30 minutes while other models take about 5-6 hours, roughly 18 times faster per frame on average.

The demonstrated scope is local atomic environments extracted from molecular dynamics simulations at environment sizes of 16, 32 and 64 neighbors, with qualitative comparisons against DGCNN predictions on fused silica shock and alpha quartz shock simulations; the models are sensitive to learning rate, layer count and hidden units, and the final models use 3 layers, 4096 hidden units and the lowest learning rate the available compute allowed.

The method is not inherently rotationally invariant; the authors suggest the network learns nearly rotationally invariant predictions because each batch is randomly rotated during training, and that explanation remains a hypothesis. The comparison with DGCNN on simulated phase fractions is qualitative, with no quantitative error reported.