A combined first-principles and data-driven approach to model building

We address a central theme of empirical model building: the incorporation of first-principles informa- tion in a data-driven model-building process. By enabling modelers to leverage all available information, regression models can be constructed using measured data along with theory-driven knowledge of response variable bounds, thermodynamic limitations, boundary conditions, and other aspects of system knowledge. We expand the inclusion of regression constraints beyond intra-parameter relationships to relation- ships between combinations of predictors and response variables. Since the functional form of these constraints is more intuitive, they can be used to reveal hidden relationships between regression param- eters that are not directly available to the modeler. First, we describe classes of a priori modeling constraints. Next, we propose a semi-infinite programming approach for the incorporation of these novel constraints. Finally, we detail several application areas and provide extensive computational results.