Gramian-based model reduction for unstable stochastic systems

Abstract This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized partial differential equations. Since asymptotic stability can often not be ensured in such a setting (e.g., due to larger noise), the main focus is on establishing model order reduction (MOR) schemes applicable unstable systems. MOR vital reduce dimension of problem lower enormous computational complexity for instance sampling methods high dimensions. In particular, new type Gramian-based approach proposed this that used very general settings. The considered Gramians are constructed identify dominant subspaces system as pointed out work. Moreover, they computed via Lyapunov However, covariance information underlying enters these equations which directly available. Therefore, efficient sampling-based relying variance techniques established derive required covariances and hence Gramians. Alternatively, an ansatz compute by deterministic approximations functions investigated. An error bound studied proved yielding priori criterion choice reduced dimension. beneficial even case. concluded numerical experiments showing efficiency schemes.