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Chapter 6 Reduced-order Modeling for Optimization Synopsis Reduced-order modeling techniques can be used in order to circumvent computational diffi- culties that arise due to large-scale state equations related to PDE-constrained optimization problems. Model reduction is one approach to generate cost-efficient low-order models which can be used as surrogate models in the optimization problems. This chapter develops a re- duced order modeling framework based on proper orthogonal decomposition (POD), which is a low-dimensional approximation to the dynamic PDE-based model. The proposed method leads to a DAE system of significantly lower order, thus replacing the one obtained from spatial discretization and making the optimization problem computationally efficient. We explain the concept of POD, the methodology to construct reduced-order models (ROMs), and motivate it with an example of Burgers equation. Further, we discuss ROM-based optimization, and describe how ROMs can be utilized to optimize in a trust-region around the point where ROM is constructed. Optimization strategy is illustrated with a hydrogen PSA case study. Chapter 6. Reduced-order Modeling for Optimization 96PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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