A technique for developing fast process models for rapid thermal processing (RTP) systems is described. The modeling strategy uses a priori knowledge of the process behavior to construct a model with relatively few unknowns. The resulting nonlinear model can then be used to extrapolate beyond the original knowledge base. Using the proper orthogonal decomposition method, the a priori information is extracted in the form of empirical eigenfunctions from transient simulation results of a detailed physically based finite element model (FEM). Low-order nonlinear models are then constructed using the empirical eigenfunctions as a basis set in a pseudospectral Galerkin approximation to the physical model, i.e., the governing partial differential equations. The predictions from models developed in this fashion show good agreement with steady-state and transient responses of the physically based FEM. In particular, the low-order models are shown to accurately replicate an actual RTP processing cycle in a typical process chamber with an order-of-magnitude reduction in computation time compared to the detailed FEM.