Solving the inverse problem of X-ray absorption spectroscopy via physics-informed deep learning

Abstract

Resolving transient atomic configurations in non-crystalline or dynamic environments remains a fundamental bottleneck in the physical sciences. While X-ray absorption spectroscopy (XAS) is a premier probe of local structure, inverting spectra into structural descriptors is a notoriously ill-posed problem due to inherent many-to-one mapping. Here, we present the Spectral Pattern Translator (SPT), a physics-informed deep learning framework that establishes a robust bridge between large-scale theoretical datasets and experimental reality. Our strategy exploits the Fourier duality between spectral energy oscillations and spatial scattering paths to overcome the "simulation-to-experiment" gap. By decomposing spectra into frequency domains, SPT effectively isolates robust structural coordination signals from the destabilizing noise inherent in experimental data. Trained on a massive library of diverse atomic environments, this approach achieves state-of-the-art accuracy in resolving continuous phase transitions in battery cathodes and deciphering local order in amorphous materials. With millisecond-scale latency, SPT removes the primary computational barrier to autonomous materials discovery, establishing a robust, noise-resilient engine for closed-loop robotic chemistry.

Figures (8)

• Figure 1: Architecture of the Spectral Pattern Translator (SPT). (a) Raw spectral data is preprocessed to extract key feature points, normalized, and encoded into initial spectral sequence vectors. (b) Dominant frequencies are identified via Fast Fourier Transform (FFT) on the spectral sequence. These components are reshaped into a two-dimensional tensor and fused through a learnable spectral query mechanism. (c) Feature nodes are embedded into a spatial graph structure, establishing dynamic contextual associations with local neighbors to refine structural representations.
• Figure 2: SPT-enabled tracking of structural and electronic evolution in LiCoO$_2$ during delithiation. (a) Schematic illustration of the phase transition pathway in LiCoO$_2$ as lithium content decreases, showing the transformation from the O3 phase to the H1-3 phase. (b) Co K-edge XANES spectra and corresponding oxidation states for various lithium concentrations. (c) The accuracy of SPT in distinguishing between Co$^{3+}$ and Co$^{4+}$ states across different structural phases.
• Figure 3: SPT performance in transfer learning for descriptor prediction in amorphous structures. (a) Atomic models of representative amorphous materials, including Fe$_3$O$_4$, Li$_7$Ti$_{11}$O$_{24}$, and Li$_7$Co$_5$O$_{12}$, generated at 5000 K. Different elements are distinguished by color, highlighting the disordered atomic arrangement and compositional diversity characteristic of amorphous phases. (b, c) Comparison of the SPT performence for structural descriptors of CN, CN2, OCN and OS across the initial crystalline-trained model (blue), direct application to the amorphous dataset (yellow), and after fine-tuning on amorphous data (red).
• Figure 4: Generalization assessment of SPT framework on experimental cobalt K-edge XANES spectra. (a) Schematic of the domain alignment protocol. The workflow illustrates the bridging of theoretical calculations (Cal.) and experimental measurements (Exp.) via multi-scale feature extraction and mapping, ensuring distributional consistency between domains. (b) Spectral energy calibration. A representative comparison between the calculated and experimental K-edge spectra of $\mathrm{LiCoO_2}$, demonstrating the precise alignment of absorption edges (approx. 7720 eV) required for valid inference. (c) Prediction performance on diverse cobalt oxides. The subpanels annotate the ground truth versus predicted oxidation states.
• Figure 5: Distribution of computed K-edge XANES spectra across eight elemental species. Each panel displays the spectral density for a specific element (Li, O, P, Ti, Mn, Fe, Co, Ni) within the dataset, with the total count of constituent spectra annotated. The horizontal axis represents relative energy (eV) with respect to the absorption edge, while the vertical axis denotes normalized absorption intensity. The color gradient indicates the density of spectral lines, highlighting the dominant spectral features for each element.