[论文解读] Beyond overcomplication: a linear model suffices to decode hidden structure-property relationships in glasses

Chenyan Wang, Mouyang Cheng+1 more|arXiv (Cornell University)|Feb 5, 2026

Material Dynamics and Properties被引用 0

一句话总结

The paper proves a universal, approximately linear relation between the radial distribution function and disorder-induced vibrational properties in glasses, enabling accurate, interpretable structure-property mapping with simple linear models across diverse glassy systems.

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.

研究动机与目标

• Motivate the need for interpretable structure-property relationships in glasses amid data-driven models' black-box concerns.
• Derive a first-order perturbation theory framework that links structural disorder to phonon-derived properties.
• Propose and validate a universal linear SPR model that maps RDF to target vibrational descriptors.
• Demonstrate interpretability enhancements via regularization without sacrificing predictive accuracy.

提出的方法

• Develop a first-order perturbation theory to relate RDF g(r) perturbations to changes in the Hessian and phonon density of states.
• Formulate a linear SPR model of the form y = W_theta g + b_theta with g being the vectorized RDF and W_theta, b_theta as learnable parameters.
• Discretize g(r) into radial bins to create a size-scalable, symmetry-invariant input descriptor.
• Apply regularization (L1 and L2) to obtain sparse, interpretable weight maps that align with structural features.
• Evaluate the model on diverse glassy systems (AMC, 2D/3D LJ, SiC, CuAlZr) and compare against CNN-based approaches.
• Argue that the approach provides interpretability and data-efficiency advantages over deeper models.

实验结果

研究问题

• RQ1 Does an approximate linear relationship between RDF and disorder-induced properties hold universally across glassy systems?
• RQ2 Can a simple linear model map g(r) to phonon-derived observables (e.g., PDOS) with accuracy comparable to CNNs across different materials?
• RQ3 How does regularization influence the interpretability of the learned mapping and its alignment with physical structure?
• RQ4 To what extent does the linear SPR framework generalize to systems with varying dimensionality, bonding types, and chemical complexity?

主要发现

• A simple linear model predicting PDOS from RDF achieves predictions visually indistinguishable from a CNN for amorphous monolayer carbon.
• The linear model attains training losses comparable to or slightly higher than CNNs but with far less data and improved generalization.
• Regularization (especially L1) yields sparse weights that align RDF features with PDOS peaks, revealing scale-dependent structure–property links.
• The linear SPR accurately reproduces PDOS across AMC, 2D/3D LJ, amorphous SiC, and ternary CuAlZr, with MSE remaining small even in complex systems (~2×10^-5 for CuAlZr).
• CNNs may overfit with limited data, whereas the linear model shows robustness and efficiency due to fewer degrees of freedom.