Koopman Operator Approximation
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
A Unified Algebraic Framework for Subspace Pruning in Koopman Operator Approximation via Principal Vectors
arXiv:2603.29001v2 Announce Type: replace Abstract: Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image under the operator. To systematically minimize this error, we propose an algebraic framework for subspace pruning utilizing principal vectors.
Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations
arXiv:2605.13135v2 Announce Type: replace Abstract: The accuracy of Koopman operator approximations over finite-dimensional spaces relies critically on their invariance properties. These can be rigorously quantified via the principal angles between a candidate subspace and its image under the Koopman operator. This paper proposes a unified algebraic framework for subspace pruning designed to systematically refine the invariance error.
AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression
Announce Type: new Abstract: Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency. However, nonlinear dynamics are so complex that capturing dynamically changing nonlinear patterns and utilizing them for downstream tasks under strict time constraints is nontrivial. To bridge the gap between nonlinear complexity and computational tractability, this study applies Koopman...
Coordinate-wise splitting algorithms for ODE simulation via Koopman-Lie product formulas
arXiv:2506.17524v3 Announce Type: replace Abstract: We present a computational framework for simulating finite-dimensional ordinary differential equations by combining classical Koopman-Lie product formulas with coordinate-wise frozen subflows. The setting is model-known, since the vector field is assumed to be available, and no data-driven approximation of the Koopman operator is attempted. Under standard assumptions, the Koopman-Lie generator associated with the flow admits a coordinate...
Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error
arXiv:2605.31438v1 Announce Type: new Abstract: Time series forecasting often requires learning nonlinear and time-delayed dependencies. A paradigmatic class of forecasting models are nonlinear vector autoregressive processes (NVAR), also known as next-generation reservoir computers (NG-RCs). These models approximate the Koopman operator on the space spanned by their explicit feature library.
Koopman Subspace Pruning in Reproducing Kernel Hilbert Spaces via Principal Vectors
arXiv:2604.01459v2 Announce Type: replace Abstract: Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning systematically discards geometrically misaligned directions to enhance this invariance proximity, which formally corresponds to the largest principal angle between the subspace and its image under the...
Excitation of control-affine systems and Koopman error bounds
arXiv:2511.03734v2 Announce Type: replace Abstract: The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems. However, extensions towards control-affine systems resulting in bilinear surrogate models are prone to demanding data requirements rendering their applicability intricate. In this paper, we propose a framework...
Input-to-State Stable Bundle Koopman Neural ODEs for Learning Controlled Dynamics under Environmental Constraints
Announce Type: new Abstract: We propose ISS-BKNO, a unified framework that integrates Koopman operator identification, Neural ordinary differential equations (ODEs), fiber bundle geometry, and input-to-state stability (ISS) certification. Unlike prior approaches that address stability, extrinsic inputs, or environmental constraints in isolation, the proposed framework simultaneously learns controlled nonlinear dynamics while guaranteeing global convergence and a computable ISS gain. The...
Certified Neural Approximations of Nonlinear Dynamics
arXiv:2505.15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of neural approximations requires formal bounds on their closeness to the underlying system. To address this fundamental challenge, we propose a novel, adaptive, and parallelizable verification method based...