Model reduction of controlled Fokker--Planck and Liouville-von Neumann equations
For researchers in control theory and quantum/statistical mechanics, this provides a practical comparison of model reduction techniques for complex bilinear systems.
The paper compares model reduction methods for bilinear control systems, specifically for Liouville-von Neumann and Fokker-Planck equations, showing that balancing-based and H2-optimal methods are competitive for large-scale examples while preserving structure and stability.
Model reduction methods for bilinear control systems are compared by means of practical examples of Liouville-von Neumann and Fokker--Planck type. Methods based on balancing generalized system Gramians and on minimizing an H2-type cost functional are considered. The focus is on the numerical implementation and a thorough comparison of the methods. Structure and stability preservation are investigated, and the competitiveness of the approaches is shown for practically relevant, large-scale examples.