Nonlinear Model Reduction via Discrete Empirical Interpolation

This thesis proposes a model reduction technique for nonlinear dynamical systems based upon combining Proper Orthogonal Decomposition (POD) and a new method, called the Discrete Empirical Interpolation Method (DEIM). The popular method of Galerkin projection with POD basis reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term generally remains that of the original problem. DEIM, a discrete variant of the approach from [11], is introduced and shown to effectively overcome this complexity issue. State space error estimates for POD-DEIM reduced systems are also derived. These [Special characters omitted.] error estimates reflect the POD…