Non-Intrusive Data-Driven Implementations of IRKA and Balanced Truncation

However, traditional implementations require full access to system matrices, making them intrusive and often impractical in real-world scenarios. This blog explores novel non-intrusive data-driven approaches that enable MOR without requiring a full system model.

Challenges in Traditional MOR

Conventional MOR methods rely on explicit knowledge of the state-space representation, which presents several challenges:

• Limited access to system matrices: In many practical cases, only input-output data is available.
• Computational complexity: Standard techniques involve solving large-scale Lyapunov equations.
• Inflexibility in discrete-time systems: Direct adaptation to discrete-time models is often non-trivial.

The Proposed Non-Intrusive Framework

This research introduces novel quadrature-based and low-rank approximation techniques to enable MOR without direct access to system matrices. Key contributions include:

• Quadrature-based balanced truncation: Approximates Gramians using frequency response data, eliminating the need for full matrix knowledge.
• Data-driven IRKA implementation: Iteratively refines interpolation points using transfer function samples without state-space realization.
• Adaptation to discrete-time systems: Extends these approaches to discrete-time settings using impulse response data.

Experimental Results and Key Insights

The proposed non-intrusive implementations were tested on benchmark systems, demonstrating:

• Comparable accuracy to traditional methods while significantly reducing computational requirements.
• Robustness across both continuous and discrete-time models.
• Elimination of the need for explicit state-space formulations, making MOR more accessible for real-world applications.

Conclusion

This work marks a significant step toward practical and scalable model order reduction, especially for systems where full access to matrices is infeasible. By leveraging data-driven methodologies, these non-intrusive approaches pave the way for efficient MOR in diverse applications such as control systems, circuit design, and fluid dynamics.

How do you see data-driven MOR transforming system analysis in your field? Let’s discuss in the comments!