Multi-fidelity framework and uncertainty quantification for thermal conductivities of aluminum alloys

Abstract

Building surrogate models to predict thermal conductivity as a function of composition and temperature is essential for a wide range of applications from material design and optimization to uncertainty quantification. However, experimental measurements of thermal conductivity are often time-consuming and costly, making it feasible to conduct only a limited number of tests. Unfortunately, the available data are grossly insufficient for training machine learning models. In this work, we present a novel approach for constructing thermal conductivity surrogate models using very few experimental measurements. Specifically, we develop CALPHAD (Calculation of Phase Diagrams) models for predicting thermal conductivity. While CALPHAD predictions alone may not achieve the necessary accuracy due to the simplifying assumptions utilized in their development, they offer a significant advantage: once built, these models can be evaluated at a low cost, allowing for the generation of a large number of predictions. To leverage this, we develop Bayesian multi-fidelity models based on Gaussian process regression that integrate a few high-fidelity experimental measurements with a set of high-throughput CALPHAD predictions with low-fidelity. We investigate this approach by considering a binary system, Al–Cu, and a ternary system, Al–Cu–Zn. We train a single-fidelity Gaussian process model based solely on high-fidelity data (experimental), and a multi-fidelity model is trained using a combination of high-fidelity and low-fidelity data.