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.
Bollt, and Ioannis G
4 Pith papers cite this work, alongside 431 external citations. Polarity classification is still indexing.
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Nowhere-vanishing Koopman eigenfunctions form a multiplicative group, enabling polynomial extensions from principal ones to enrich eigenspaces and enable global representations from local data in multistable systems.
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.
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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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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On the algebra of Koopman eigenfunctions and on some of their infinities
Nowhere-vanishing Koopman eigenfunctions form a multiplicative group, enabling polynomial extensions from principal ones to enrich eigenspaces and enable global representations from local data in multistable systems.
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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.