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Physical processes described by partial di® erential equations (PDE's) are usu-ally simulated by discretizing the spatial and the temporal domain of the variables (temperature, velocity). In this way, numerical approximations of the dynamic behavior of these processes are obtained. As a general rule, the ner the discretization, the more accurate the numerical solution of the PDE's will be. However, a ne discretization leads to a large number of equations which need to be solved simultaneously at every time step. Hence, the model complexity increases with increasing requirements on model accuracy. The objective of this PhD thesis is to develop generic methods to reduce the complexity of a system of PDE's to not more than 100 equations. In doing so, the reduced model should maintain a maximum level of accuracy, while for simulation purposes it is desired that the computational speed of the reduced order model is at least 50 times faster1 than real-time. The last requirement is relevant for the synthesis of (real-time) dynamic optimization. In this thesis, mainly models for heat conduction of conductive and convective processes are considered, with a focus on applications in glass furnaces. A technique based on the orthogonal decomposition of a collection of measure-ments of physical quantities (such as temperature) in position and time (sig-nals) is used to reduce the complexity of models. Following ideas from Fourier series expansions, signals are represented as series of orthonormal functions. These so-called basis functions approximate the spatial distribution of the signal while the coe±cients of the basis functions represent the time-varying …