A self-explainable operator learning method reformulates operators as decomposable integral equations to reveal spatial input contributions to predictions in blood flow and aerodynamics problems.
2015 A kernel-based method for data- driven koopman spectral analysis.Journal of Computational Dynamics2, 247–265
6 Pith papers cite this work. Polarity classification is still indexing.
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2026 6representative citing papers
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.
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 data-driven ABL flux parameterization using convolution operators on mean profiles, trained and tested on LES, improves on standard K-profile closures while remaining interpretable.
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.
citing papers explorer
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Self-explainable Operator Learning for Discovering Spatial Patterns in Functional Data
A self-explainable operator learning method reformulates operators as decomposable integral equations to reveal spatial input contributions to predictions in blood flow and aerodynamics problems.
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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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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 Flux Parameterization for the Atmospheric Boundary Layer
A data-driven ABL flux parameterization using convolution operators on mean profiles, trained and tested on LES, improves on standard K-profile closures while remaining interpretable.
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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.