Empirical model reduction of differential-algebraic equation systems

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This thesis focuses on reducing differential-algebraic equation (DAE) systems, which often arise in modeling physical or chemical processes and can lead to large equation systems. Such large models can result in lengthy simulation times, particularly in real-time applications. To address this, the thesis introduces a novel method based on proper orthogonal decomposition (POD) for reducing both linear and nonlinear DAE systems, demonstrating improved performance over existing POD methods. The proposed approach involves transforming the DAE system into a dynamic subsystem and an algebraic subsystem before applying a Galerkin Projection for reduction. This method generalizes the connection between POD reduction and balanced truncation, which is typically used for ordinary differential equation (ODE) systems, to DAE systems. Notably, the proposed method can handle linear DAE systems with any differential index, overcoming limitations of previous POD methods that struggle with higher indices. Additionally, the method is successfully applied to a nonlinear DAE system with a strangeness index of zero, where traditional methods may fail. To further enhance efficiency, a grey-box modeling approach is suggested, which substitutes numerous computationally intensive nonlinear functions with fewer parameterized nonlinear functions, potentially reducing simulation times.