Application of the Maximum Entropy Method to Multifunctional Materials for Data Fusion and Uncertainty Quantification

Bayesian statistics is a quintessential tool for model validation in many applications including smart materials, adaptive structures, and intelligent systems. It typically uses either experimental data or high-fidelity simulations to infer model parameter uncertainty of reduced order models due to experimental noise and homogenization of quantum or atomistic behavior. When heterogeneous data is available for Bayesian inference, open questions remain on appropriate methods to fuse data and avoid inappropriate weighting on individual data sets. To address this issue, we implement a Bayesian statistical method that begins with maximizing entropy. We show how this method can weight heterogeneous data automatically during the inference process through the error covariance. This Maximum Entropy (ME) method is demonstrated by quantifying uncertainty in 1) a ferroelectric domain structure model and 2) a finite deforming electrostrictive membrane model. The ferroelectric phase field model identifies continuum parameters from multiple density functional theory calculations. In the case of the electrostrictive membrane, parameters are estimated from both mechanical and electric displacement experimental measurements.