System, method and computer program product including instructions executed by a processor system for configuring and controlling a facility to perform a manufacturing process and updating a tool controlling the process according to a model employed for mapping calculated coefficients that characterize non-linear variations observed of a product to actual control parameters governing the processes/tools used by the facility during the manufacturing process. In a semiconductor manufacturing process, the method enables real-time control of variation in an exposure step of a patterning process using an exposure tool to minimize a nonlinear variation in one or more pattern attributes by adjusting the exposure tool or the patterning process corresponding to the calculated coefficients. In the method, measurements of product attributes, obtained by finite sampling over a well defined domain (e.g., a region such as a field/wafer in lithographic patterning), are projected onto a predefined reference mesh spanning the domain, using a physically based model comprised of functions constructed to be orthogonal and normalized over a discrete set of reference mesh locations.