Physics-Informed Symbolic Regression for Predicting the Glass Transition Temperature of Alkali Borate Glasses

Abstract

The glass transition temperature ($T_g$) of alkali borate glasses is strongly composition-dependent and difficult to predict from first principles due to the structural complexity of the boron network. Here, we apply physics-informed symbolic regression (combining evolutive search with physically meaningful descriptors) to derive an interpretable closed-form expression for $T_g$ in the $x{\mathrm{M}}_2\mathrm{O}\cdot (100-x){\mathrm{B}}_2{\mathrm{O}}_3$ glass family, with M = Li, Na, and K and $x$ expressed in mol%, and subsequently extrapolate it to M = Rb and Cs. The resulting model achieves a root-mean-square error of 14-16 K while maintaining clear physical interpretability, explicitly capturing the interplay among $T_g$, structural dissociation energy, and network packing. Critically, models built on the Rigid Unit Packing Fraction (RUPF) yield substantially more realistic $T_g$ predictions than those using the conventional Atomic Packing Fraction (APF), as APF overestimates structural rigidity at intermediate compositions. The fitted dissociation energies are further validated against the revised Makishima-Mackenzie model, confirming that the inferred parameters are physically consistent, not merely statistically effective, within the alkali borate family. Finally, Monte Carlo uncertainty quantification reveals that prediction uncertainty is highest in the compositional regions associated with the boron anomaly, directly linking model limitations to a known structural transition in these glasses. This result highlights the potential of physics-informed symbolic regression as a transparent and interpretable alternative to black-box models for property prediction in glass systems.

21 pages, 3 figures