Model reduction of multi-variable distributed systems through empirical projection spaces

This paper considers the problem of finding optimal projection spaces for the calculation of reduced order models for distributed systems. The method of proper orthogonal decompositions is popular in the reduction of fluid dynamics models, but may become rather cumbersome for the reduction of systems in which the total dimension of physical variables is large. This paper aims to deal with this problem and proposes the construction of projection spaces from tensor representations of observed, measured or simulated data. The method is illustrated for the reduced order modeling of a tubular reactor.