AI 中文总结
针对碱金属硼酸盐玻璃$T_g$难预测的问题，本研究采用物理启发符号回归推导了具物理可解释性的$T_g$闭式表达式，验证了参数物理一致性，明确了模型不确定性与硼异常的关联，为玻璃性能预测提供了新的透明建模方案。
AI 中文摘要
碱金属硼酸盐玻璃的玻璃化转变温度（$T_{g}$）具有强烈的成分依赖性，且由于硼网络的结构复杂性，难以通过第一性原理进行预测。本文中，我们应用物理启发符号回归（将进化搜索与具有物理意义的描述符相结合），推导了$x\text{M}_2\text{O}\text{·}(100-x)\text{B}_2\text{O}_3$玻璃体系中$T_{g}$的可解释闭式表达式，其中M为Li、Na、K，$x$的单位为mol%，随后将该表达式外推至M为Rb和Cs的情况。所得模型的均方根误差为14-16 K，同时保持了清晰的物理可解释性，明确捕捉了$T_{g}$、结构解离能与网络堆积之间的相互作用。关键的是，基于刚性单元堆积分数（RUPF）构建的模型比使用传统原子堆积分数（APF）的模型能给出更符合实际的$T_{g}$预测，因为APF会高估中间成分下的结构刚度。拟合得到的解离能进一步经修正的Makishima-Mackenzie模型验证，证实了推断的参数在碱金属硼酸盐体系内具有物理一致性，而非仅具有统计有效性。最后，蒙特卡洛不确定性量化表明，与硼异常相关的成分区域预测不确定性最高，这直接将模型的局限性与这些玻璃中已知的结构转变联系起来。该结果凸显了物理启发符号回归作为黑箱模型的透明、可解释替代方案，在玻璃体系性能预测中的潜力。
英文摘要
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.
Comments21 pages, 3 figures
