The paper introduces diagnostic certificates that separately assess state-space coverage, lifted-feature nondegeneracy, and regression-spectrum quality for Koopman and EDMDc identification, with theoretical guarantees on the smallest singular value under a population spectral gap.
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and Kevrekidis, Ioannis G
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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.
SILAS jointly optimizes polynomial ODE vector fields and polynomial Lyapunov functions from data to produce models with provably bounded trajectories via compact absorbing sets.
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.
Introduces finite-lag operator geometry deriving a source-centered transport tensor that decomposes into spread and coherent displacement plus an antisymmetric circulation measure, with proofs of covariance and stability.
A kernel-based data-driven optimization method computes optimal perturbations to control the spectrum of transfer operators in high-dimensional dynamical systems.
Data-driven Koopman analysis of a bistable stochastic system recovers large deviation theory escape time statistics and basin structure via the subdominant mode.
Commutativity regularization mitigates transient error amplification in autoregressive neural simulators by penalizing non-normality and non-commutativity of Jacobians, yielding stable long-horizon rollouts.
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.
Connects continuum stochastic signals to graphon random walks via Koopman and Perron-Frobenius operators for spectral clustering and graphon reconstruction from data.
Optimizing the activation function in randomized neural networks provides a more suitable dictionary for transfer operator approximation in stochastic differential equations and random walks on graphons.
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.
LaLQR learns a latent linear-quadratic representation of robotic systems by imitating MPC to enable efficient LQR control.
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Diagnostic Certificates of Data Quality and Regression Identifiability for Koopman Identification
The paper introduces diagnostic certificates that separately assess state-space coverage, lifted-feature nondegeneracy, and regression-spectrum quality for Koopman and EDMDc identification, with theoretical guarantees on the smallest singular value under a population spectral gap.
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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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Data-driven discovery of polynomial ODEs with provably bounded solutions
SILAS jointly optimizes polynomial ODE vector fields and polynomial Lyapunov functions from data to produce models with provably bounded trajectories via compact absorbing sets.
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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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Finite-Lag Operator Geometry of Recurrent Representations
Introduces finite-lag operator geometry deriving a source-centered transport tensor that decomposes into spread and coherent displacement plus an antisymmetric circulation measure, with proofs of covariance and stability.
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Data-driven methods for computation of optimal linear response in high-dimensional dynamical systems
A kernel-based data-driven optimization method computes optimal perturbations to control the spectrum of transfer operators in high-dimensional dynamical systems.
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Data-driven analysis of metastability in a stochastic bistable system
Data-driven Koopman analysis of a bistable stochastic system recovers large deviation theory escape time statistics and basin structure via the subdominant mode.
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Controlling Transient Amplification Improves Long-horizon Rollouts
Commutativity regularization mitigates transient error amplification in autoregressive neural simulators by penalizing non-normality and non-commutativity of Jacobians, yielding stable long-horizon rollouts.
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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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Learning graphons from data: Random walks, transfer operators, and spectral clustering
Connects continuum stochastic signals to graphon random walks via Koopman and Perron-Frobenius operators for spectral clustering and graphon reconstruction from data.
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Optimization of randomized neural networks for transfer operator approximation
Optimizing the activation function in randomized neural networks provides a more suitable dictionary for transfer operator approximation in stochastic differential equations and random walks on graphons.
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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.
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Latent Linear Quadratic Regulator for Robotic Control Tasks
LaLQR learns a latent linear-quadratic representation of robotic systems by imitating MPC to enable efficient LQR control.