For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
Spectral properties of dynamical systems, model reduction and decompositions
8 Pith papers cite this work. Polarity classification is still indexing.
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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.
Koopman autoencoders with forcings and temporal unrolling deliver accurate year-long predictions for coastal-ocean models at 300-1400x speedup, outperforming POD in two of three cases.
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.
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.
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.
citing papers explorer
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Solving linear-rate ODE hierarchies (like master equations) using closures and operator splitting
For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
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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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Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models
Koopman autoencoders with forcings and temporal unrolling deliver accurate year-long predictions for coastal-ocean models at 300-1400x speedup, outperforming POD in two of three cases.
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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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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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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.