Deep-Koopman-KANDy recovers symbolic Koopman dictionaries post-training by replacing the encoder and decoder with KANs and applying a level-set construction with chain-rule gradients, achieving high recall on Lorenz and expected behavior on other maps.
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A novel identity connects reduced-model drift and diffusion to the conditional score of the finite-time transition density, turning calibration into a least-squares problem over stationary lagged pairs that preserves invariant statistics and dynamical correlations.
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
Extends linear response theory to nonautonomous systems and applies it to optimal fingerprinting for attributing changes to multiple forcings in time-dependent backgrounds, with numerical tests on a climate model.
Koopman latent space representations from early epidemic simulation data enable accurate prediction of major outbreaks and identification of minimal single-agent interventions to prevent them.
A theoretical framework establishing representer theorems, Sobolev approximation bounds, and spectral convergence for kernel-based learning of spatio-temporal dynamical systems using OV RKHS and Koopman approximations.
citing papers explorer
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Deep-Koopman-KANDy: Dictionary Discovery for Deep-Koopman Operators with Kolmogorov-Arnold Networks for Dynamics
Deep-Koopman-KANDy recovers symbolic Koopman dictionaries post-training by replacing the encoder and decoder with KANs and applying a level-set construction with chain-rule gradients, achieving high recall on Lorenz and expected behavior on other maps.
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Conditional Score-Based Modeling of Effective Langevin Dynamics
A novel identity connects reduced-model drift and diffusion to the conditional score of the finite-time transition density, turning calibration into a least-squares problem over stationary lagged pairs that preserves invariant statistics and dynamical correlations.
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Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
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Linear Response and Optimal Fingerprinting for Nonautonomous Systems
Extends linear response theory to nonautonomous systems and applies it to optimal fingerprinting for attributing changes to multiple forcings in time-dependent backgrounds, with numerical tests on a climate model.
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Koopman Representations for Early Outbreak Warning and Minimal Counterfactual Intervention in Multi-Agent Epidemic Simulations
Koopman latent space representations from early epidemic simulation data enable accurate prediction of major outbreaks and identification of minimal single-agent interventions to prevent them.
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Spatio-Temporal Prediction via Operator-Valued RKHS and Koopman Approximation
A theoretical framework establishing representer theorems, Sobolev approximation bounds, and spectral convergence for kernel-based learning of spatio-temporal dynamical systems using OV RKHS and Koopman approximations.