Model order reduction
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Many modern mathematical models of real-life processes pose challenges when used in numerical simulations, due to complexity and large size (dimension). Model order reduction aims to lower the computational complexity of such problems, for example, in simulations of large-scale dynamical systems and control systems. By a reduction of the model's associated state space dimension or degrees of freedom, an approximation to the original model is computed. This reduced-order model (ROM) can then be evaluated with lower accuracy but in significantly less time.
A common approach for model order reduction is projection-based reduction. The following methods fall into this class:
- Proper Orthogonal Decomposition
- Balanced Truncation
- Approximate Balancing
- Reduced Basis Method
- Matrix Interpolation
- Transfer Function Interpolation
- Piecewise Tangential Interpolation
- Loewner Framework
- (Empirical) Cross Gramian
- Krylov Subspace methods
- Bai, Zhaojun (2002). "Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems". Applied Numerical Mathematics. 43: 9–44.
- Antoulas, Athanasios C. (2005). Approximation of Large-Scale Dynamical Systems. SIAM. ISBN 978-0-89871-529-3. doi:10.1137/1.9780898718713.
- Benner, Peter; Fassbender, Heike (2014), "Model Order Reduction: Techniques and Tools", Encyclopedia of Systems and Control (PDF), Springer, ISBN 978-1-4471-5102-9, doi:10.1007/978-1-4471-5102-9_142-1
- Antoulas, Athanasios C.; Sorensen, Danny C.; Gugercin, Serkan (2006), "A survey of model reduction methods for large-scale systems" (PDF), Contemporary Mathematics, 280: 193–220
- Benner, Peter; Gugercin, Serkan; Willcox, Karen (2013), A survey of model reduction methods for parametric systems (PDF)
- Baur, Ulrike; Benner, Peter; Feng, Lihong (2014), "Model order reduction for linear and nonlinear systems: a system-theoretic perspective" (PDF), Archives of Computational Methods in Engineering, 21 (4), doi:10.1007/s11831-014-9111-2