Koopman
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
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...
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem. In computation, however, everything depends on a hard finite-dimensional choice: the observables must be expressive, nearly invariant under the dynamics, and, ideally, compatible with composition. Deep Koopman methods learn flexible coordinates, whereas structure-preserving methods enforce operator identities on fixed dictionaries.
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.
A Koopman Set-Membership Approach for Nonlinear Data-Driven Control with Stability Guarantees
arXiv:2606.01378v1 Announce Type: new Abstract: This paper proposes a data-driven controller design method for unknown nonlinear systems based on a Koopman bilinear realization. Using Koopman operator theory, the nonlinear system can be represented as a bilinear discrete-time system with a residual error term. The residual error is proportionally bounded by the norm of the lifted state and input, while the system matrices of the bilinear model are unknown.
Residual Pseudospectra Reveal a Physics-Informed Koopman Backbone for Tropical Pacific Variability and ENSO Prediction
Announce Type: new Abstract: Tropical Pacific sea-surface-temperature (SST) variability spans interacting timescales, with the ENSO as its dominant interannual expression. Yet the dynamical structure organizing this variability and underpinning extended-range predictability remains difficult to extract from high-dimensional observations. Koopman operator learning offers spectral coordinates for nonlinear dynamics, yet finite geophysical records often produce dense, sampling-sensitive spectra...
Residual Pseudospectra Reveal a Physics-Informed Koopman Backbone for Tropical Pacific Variability and ENSO Prediction
Announce Type: cross Abstract: Tropical Pacific sea-surface-temperature (SST) variability spans interacting timescales, with the ENSO as its dominant interannual expression. Yet the dynamical structure organizing this variability and underpinning extended-range predictability remains difficult to extract from high-dimensional observations. Koopman operator learning offers spectral coordinates for nonlinear dynamics, yet finite geophysical records often produce dense, sampling-sensitive...
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...
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...
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...
Koopman operator learning for predictive control via Khatri-Rao kernel regression
arXiv:2606.02938v1 Announce Type: cross Abstract: This paper develops a data-driven realization of the generalized Koopman operator (GeKo), in which states and inputs are lifted independently and the dynamics are expressed as a tensor bilinear system. The first contribution is a time-sequenced multi-step Khatri-Rao kernel regression formulation that exposes the operator to evolved snapshots along trajectories rather than only single one-step pairs, which reduces compounded prediction error....