The goal of this research program is to develop a quantum informed non-linear field theory and continuum mechanics modeling framework for multifunctional materials using advanced materials theory, computational methods, and parameter uncertainty analysis using Bayesian statistics. The computational material modeling framework will bridge fundamental nonlinear mechanics and electromagnetic field theory at the continuum scale with density functional theory (DFT) at the quantum scale. The connection between these scales will be validated through an uncertainty propagation analysis based upon adaptive Markov Chain Monte Carlo algorithms, sparse grid techniques, and Bayesian statistics.