InfPolyn, a Nonparametric Bayesian Characterization for Composition-Dependent Interdiffusion Coefficients

Abstract

Composition-dependent interdiffusion coefficients are key parameters in many physical processes. However, finding such coefficients for a system with few components is challenging due to the underdetermination of the governing diffusion equations, the lack of data in practice, and the unknown parametric form of the interdiffusion coefficients. In this work, we propose InfPolyn, Infinite Polynomial, a novel statistical framework to characterize the component-dependent interdiffusion coefficients. Our model is a generalization of the commonly used polynomial fitting method with extended model capacity and flexibility and it is combined with the numerical inversion-based Boltzmann–Matano method for the interdiffusion coefficient estimations. We assess InfPolyn on ternary and quaternary systems with predefined polynomial, exponential, and sinusoidal interdiffusion coefficients. The experiments show that InfPolyn outperforms the competitors, the SOTA numerical inversion-based Boltzmann–Matano methods, with a large margin in terms of relative error (10x more accurate). Its performance is also consistent and stable, whereas the number of samples required remains small.