Modelo de regressão simbólica informado por física para a temperatura de transição vítrea em vidros alcalino borato

Abstract

In this thesis, a new analytical model for the glass transition temperature of borate glasses of the form xM2O–(100 − x)B2O3, with M = Li, Na, and K, is proposed. The model was induced through a physics-informed symbolic regression framework. The physical descriptors employed in the induction process were based on the elastic deformation model originally proposed by Makishima and Mackenzie, in which the Young’s modulus of multicomponent glasses is expressed in terms of the average bond dissociation energy of the glass network and the manner in which atoms are structurally arranged, represented by the packing density factor. In addition, a contemporary revision of the original model was considered, introducing a new formulation of the packing factor based on rigid unit packing fraction called RUPF. The validation of the induced model was carried out through three complementary stages designed to ensure both physical and statistical rigor: (i) evaluation of the extrapolation capability to systems chemically distinct from those used in training, specifically glasses containing Rb and Cs; (ii) estimation of bond dissociation energies via error minimization with respect to experimental glass transition temperature data, followed by comparison with reference values from the literature in order to assess physical plausibility; and (iii) knowledge transfer to the prediction of the Young’s modulus of Rband Cs-containing glasses using the model proposed by Shi et al. The results from these three validation stages indicate that the induced model is physically consistent, as the estimated bond dissociation energies fall within physically reasonable ranges, while also exhibiting good statistical accuracy, with mean deviations on the order of 17 K relative to experimental Tg values between 300 and 800K. The limitations of the model were further investigated along two fronts: (i) uncertainty analysis through Monte Carlo uncertainty propagation and (ii) extrapolation to systems containing divalent modifiers, specifically Sr and Ba. A region of increased uncertainty was observed in the compositional range between 20% and 40% alkali addition, which was attributed to the larger uncertainties associated with the dissociation energies of BO4 structural units characteristic of this range. Extrapolation to alkaline-earth modifiers revealed a clear limitation of the model, which systematically underestimated the glass transition temperature by more than 100 K for both systems. Overall, this thesis demonstrates a methodological framework capable of inducing data-driven, physics-informed analytical models that exhibit physical consistency by extrapolating beyond the physical-chemical domain used in training and by transferring knowledge to simillar property models. This approach establishes a promising pathway for the development of interpretable models capable of generating new physical insight from experimental data.