# Predicting densities and elastic moduli of SiO2-based glasses from a statistical and data science perspective

# Predicting densities and elastic moduli of SiO2-based glasses from a statistical and data science perspective

**Abstract. **To address the challenge of predicting elastic moduli in SiO₂-based glasses with high precision and efficiency, we leveraged machine learning (ML) methods across an extensive compositional space involving over ten types of additive oxides beyond SiO₂. Traditionally, deriving a universal predictive expression for elastic moduli has been challenging due to the complex dependency on interatomic bonds and structural ordering across multiple length scales. By utilizing a machine learning framework, we demonstrate a robust model that accurately predicts densities and elastic moduli of SiO₂-based glasses prior to synthesis. In addition to the machine learning approaches, we propose new methods to a more general situation using measurement error models and covariate shift techniques. Measurement error models are particularly useful for predicting the material science problem because of the high cost of real experiment and biased numerical inputs. To further handle discrepancies between the experimental and numerical inputs, we elaborate the idea of covariate shift. Together, these statistical enhancements reinforce our model's predictive power, allowing it to handle real-world variability and compositional complexity with greater precision, enabling more reliable exploration and optimization of multicomponent SiO₂-based glass systems, even other material systems.