A Heteroscedastic Gaussian Process Regression Workflow for Materials Property Prediction in Molecular Simulations

The field of computational materials science faces various challenges in data processing, including dealing with high-dimensional phase spaces, multi-parameter vectors, and error analysis. In particular, uncertainty quantification of models that fit large materials datasets has become crucial for making informed engineering decisions. Gaussian Process Regression (GPR) has gained popularity in this task compared to physical-based parametric models due to its flexibility and ability to naturally predict errors. In this talk, we focus on the self-diffusion coefficient dataset generated through Green-Kubo and Einstein's Relation during the post-processing of the molecular-dynamics (MD) dataset. We present a heteroscedastic GPR workflow for predicting the fluid self-diffusion coefficient. This workflow evaluates the mean and variance for fluid diffusivity as a function of density. Unlike the standard GPR framework, the proposed approach adapts local uncertainties into the model, making it more flexible in reflecting the non-constant variance nature of the MD dataset. We also show the extensions of the GPR model on the higher dimensional MD dataset for multiple features like the temperature and pressure.