XANE(3): An E(3)-Equivariant Graph Neural Network for Accurate Prediction of XANES Spectra from Atomic Structures

We present XANE(3), a physics-based E(3)-equivariant graph neural network for predicting X-ray absorption near-edge structure (XANES) spectra directly from atomic structures. The model combines tensor-product message passing with spherical harmonic edge features, absorber-query attention pooling, custom equivariant layer normalization, adaptive gated residual connections, and a spectral readout based on a multi-scale Gaussian basis with an optional sigmoidal background term. To improve line-shape fidelity, training is performed with a composite objective that includes pointwise spectral reconstruction together with first- and second-derivative matching terms. We evaluate the model on a dataset of 5,941 FDMNES simulations of iron oxide surface facets and obtain a spectrum mean squared error of $1.0 \times 10^{-3}$ on the test set. The model accurately reproduces the main edge structure, relative peak intensities, pre-edge features, and post-edge oscillations. Ablation studies show that the derivative-aware objective, custom equivariant normalization, absorber-conditioned attention pooling, adaptive gated residual mixing, and global background term each improve performance. Interestingly, a capacity-matched scalar-only variant achieves comparable pointwise reconstruction error but reduced derivative-level fidelity, indicating that explicit tensorial channels are not strictly required for low intensity error on this dataset, although they remain beneficial for capturing finer spectral structure. These results establish XANE(3) as an accurate and efficient surrogate for XANES simulation and offer a promising route toward accelerated spectral prediction, ML-assisted spectroscopy, and data-driven materials discovery.