Predictive modeling of coupled multi-physics systems: I. Theory

• We developed “predictive modeling of coupled multi-physics systems (PMCMPS)”.
• PMCMPS reduces predicted uncertainties in predicted model responses and parameters.
• PMCMPS treats efficiently very large coupled systems.

This work presents an innovative mathematical methodology for “predictive modeling of coupled multi-physics systems (PMCMPS).” This methodology takes into account fully the coupling terms between the systems but requires only the computational resources that would be needed to perform predictive modeling on each system separately. The PMCMPS methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution based on a priori known mean values and uncertainties characterizing the parameters and responses for both multi-physics models. This “maximum entropy”-approximate a priori distribution is combined, using Bayes’ theorem, with the “likelihood” provided by the multi-physics simulation models. Subsequently, the posterior distribution thus obtained is evaluated using the saddle-point method to obtain analytical expressions for the optimally predicted values for the multi-physics models parameters and responses along with corresponding reduced uncertainties.Noteworthy, the predictive modeling methodology for the coupled systems is constructed such that the systems can be considered sequentially rather than simultaneously, while preserving exactly the same results as if the systems were treated simultaneously. Consequently, very large coupled systems, which could perhaps exceed available computational resources if treated simultaneously, can be treated with the PMCMPS methodology presented in this work sequentially and without any loss of generality or information, requiring just the resources that would be needed if the systems were treated sequentially.