Beyond overcomplication: a linear model suffices to decode hidden structure-property relationships in glasses

TL;DR

The paper tackles the challenge of decoding structure-property relationships in glasses with interpretable, data-efficient models. It derives a universal linear relation between the radial distribution function and disorder-driven spectral properties via first-order perturbation theory, and implements a linear SPR model with y_hat = W g + b trained across diverse glass types. Across amorphous monolayer carbon, Lennard-Jones glasses, amorphous SiC, and CuAlZr alloys, the linear approach achieves predictive accuracy competitive with CNNs while requiring less data and offering clear interpretability through regularized weights that map RDF features to vibrational signatures. This framework suggests a unifying, physics-grounded method for cross-modal inferences between diffraction-based structural descriptors and vibrational observables, with broad implications for glassy materials design and analysis.

Abstract

Establishing reliable and interpretable structure-property relationships in glasses is a longstanding challenge in condensed matter physics. While modern data-driven machine learning techniques have proven highly effective in establishing structure-property correlations, many models are criticized for lacking physical interpretability and being task-specific. In this work, we identify an approximate linear relation between structure profiles and disorder-induced responses of glass properties based on first order perturbation theory. We analytically demonstrate that this relationship holds universally across glassy systems with varying dimensions and distinct interaction types. This robust theoretical relationship motivates the adoption of linear machine learning models, which we show numerically to achieve surprisingly high predictive accuracy for structure-property mapping in a wide variety of glassy materials. We further devise regularization analysis to further enhance the interpretability of our model, bridging the gap between predictive performance and physical insight. Overall, this linear relation establishes a simple yet powerful connection between structural disorder and spectral properties in glasses, opening a new avenue for advancing their studies.

Figures (4)

• Figure 1: Universal linear SPR for phonon-related properties of amorphous materials.(a) Representative amorphous systems considered in this work, including unary amorphous monolayers, binary and ternary bulk glasses, and high-entropy alloys, spanning a wide range of structural disorder. (b) Atomic configurations are encoded using RDF $g(r)$, which captures two-body structural correlations in a symmetry-invariant and size-scalable manner. (c) A simple linear SPR model maps the vectorized $g(r)$ to target property features $y$ through learnable weight ($W_\theta$) and bias ($b_\theta$) parameters shared across all structures. (d) The resulting framework enables the prediction of multiple phonon-derived observables, such as PDOS, Raman spectrum, INS and IXS spectrum.
• Figure 2: Structures, RDF, and PDOS of AMC with varying disorder and PDOS prediction results. Representative AMC structures with increasing degrees of disorder are shown from left to right, together with their corresponding RDF and PDOS. Columns span a structural continuum from crystalline-like to highly amorphous configurations. Atomic structures are colored according to ring statistics and local bonding environments: six-membered rings are shown in green (bright green denotes a six-membered ring that has at least one nearest-neighboring six-membered ring whose nearest-neighbors are all six-membered, while the remaining six-membered rings are colored dark green); five-, seven-, and eight-/nine-membered rings are shown in red, blue, and purple, respectively. Vacancies are rendered transparent. For each AMC structure, the PDOS predicted by a linear model and by CNN are compared against the reference PDOS obtained from calculations in the third row, illustrating the predictive performance of the two models across different levels of structural disorder.
• Figure 3: Visualization of weights for the linear SPR mapping of amorphous monolayer carbon. Learned linear weights are shown in a heat map for a representative AMC structure, using L1 and L2 regularized weights $\alpha=10^{-5},\ \beta=0$, respectively. The colored regions indicate non-zero weights, and the dashed lines indicate the correspondence between the peaks of RDF and PDOS. The reference RDF and PDOS showed above are corresponding to a moderate disorder structure.
• Figure 4: Linear structure–property relation across disordered systems of increasing complexity. Representative atomic configurations (first column), RDF ($g(r)$) (second column), and corresponding PDOS (third column) are shown for four disordered systems: 2D LJ, 3D LJ, binary covalent SiC, and ternary metallic CuAlZr. Red curves correspond to the highly disordered structures shown in the first column, and the blue curves represent the RDF and PDOS of the crystalline phases. Solid curves denote reference data, while dashed curves indicate predictions of the linear model. The rightmost column compares test MSE of the linear model and CNN.