Intro
Preface
Contents
*-20pt Methods and Techniques of Model Order Reduction
On Bilinear Time-Domain Identification and Reduction in the Loewner Framework
1 Introduction
1.1 Outline of the Paper
2 System Theory Preliminaries
2.1 Linear Systems
2.2 Nonlinear Systems
3 The Loewner Framework
3.1 The Loewner Matrix
3.2 Construction of Interpolants
4 The Special Case of Bilinear Systems
4.1 The Growing Exponential Approach
4.2 The Kernel Separation Method
4.3 Identification of the Matrix N
4.4 A Separation Strategy for the second Kernel

4.5 The Loewner-Volterra Algorithm for Time-Domain Bilinear Identification and Reduction
4.6 Computational Effort of the Proposed Method
5 Numerical Examples
6 Conclusion
References
Balanced Truncation for Parametric Linear Systems Using Interpolation of Gramians: A Comparison of Algebraic and Geometric Approaches
1 Introduction
2 Balanced Truncation for Parametric Linear Systems and Standard Interpolation
2.1 Balanced Truncation
2.2 Interpolation of Gramians for Parametric Model Order Reduction
2.3 Offline-Online Decomposition

3 Interpolation on the Manifold mathcalS+(k, n)
3.1 A Quotient Geometry of mathcalS+(k, n)
3.2 Curve and Surface Interpolation on Manifolds
4 Numerical Examples
4.1 A model for heat conduction in solid material
4.2 An Anemometer Model
5 Conclusion
References
Toward Fitting Structured Nonlinear Systems by Means of Dynamic Mode Decomposition
1 Introduction
2 Dynamic Mode Decomposition
2.1 Dynamic Mode Decomposition with Control (DMDc)
2.2 Input-Output Dynamic Mode Decomposition
3 The Proposed Extensions
3.1 Bilinear Systems
3.2 Quadratic-Bilinear Systems

4 Numerical Experiments
4.1 The Viscous Burgers' Equation
4.2 Coupled van der Pol Oscillators
5 Conclusion
6 Appendix
6.1 Computation of the Reduced-Order Matrices for the Quadratic-Bilinear Case
References
Clustering-Based Model Order Reduction for Nonlinear Network Systems
1 Introduction
2 Preliminaries
2.1 Graph Theory
2.2 Graph Partitions
2.3 Linear Multi-agent Systems
2.4 Clustering-Based Model Order Reduction
2.5 Model Reduction for Non-asymptotically Stable Systems
3 Clustering for Linear Multi-agent Systems

4 Clustering for Nonlinear Multi-agent Systems
4.1 Nonlinear Multi-agent Systems
4.2 Clustering by Projection
5 Numerical Examples
5.1 Small Network Example
5.2 van der Pol Oscillators
6 Conclusions
References
Adaptive Interpolatory MOR by Learning the Error Estimator in the Parameter Domain
1 Introduction
2 Interpolatory MOR
3 Greedy Method for Choosing Interpolation Points
4 Adaptive Training by Learning the Error Estimator in the Parameter Domain
4.1 Radial Basis Functions
4.2 Learning the Error Estimator over the Parameter Domain