Shah & Cortés' subspace pruning cuts Koopman computation by 10x

Koopman operator approximations are vital for modeling nonlinear dynamical systems, but their accuracy depends heavily on the invariance of finite-dimensional subspaces. In a new preprint on arXiv, researchers Dhruv Shah and Jorge Cortés propose a unified algebraic framework for subspace pruning that systematically refines invariance error using principal angles between candidate subspaces and their Koopman images. The key insight is a geometric equivalence between consistency-based methods and principal-vector pruning, enabling a hybrid strategy that switches between multiple and single principal vector pruning for improved numerical stability and scalability.

The authors derive rigorous error bounds for retention of approximate and external eigenfunctions, showing that the multi-vector approach mitigates numerical drift inherent in sequential pruning. To ensure scalability, they develop an efficient numerical update scheme based on rank-one modifications that reduces the computational complexity of tracking principal angles by an order of magnitude—a critical advance for high-dimensional systems. Finally, they exploit the pruned subspace to build lifted linear models for state prediction, explicitly accounting for trade-offs between improving invariance and minimizing reconstruction error. Simulations demonstrate the effectiveness across multiple benchmarks, making this a practical tool for control systems and AI-driven dynamics modeling.