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.
V AMPnets for deep learning of molecular kinetics.Nature Communications, 9(1):5, 2018
5 Pith papers cite this work, alongside 477 external citations. Polarity classification is still indexing.
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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.
DPA provides closed-form relation from level-set geometry to data score and proves extra latent components are conditionally independent, revealing intrinsic dimension.
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.
Q-GAIN is a Python package implementing ML classification, object detection, and physics-informed metrics for analyzing images of atomic BECs, demonstrated on MNIST, soliton detection, and vortex identification tasks.
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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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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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Distributional Autoencoders Know the Score
DPA provides closed-form relation from level-set geometry to data score and proves extra latent components are conditionally independent, revealing intrinsic dimension.
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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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Q-GAIN: A Python Package for Machine Learning and Physically Informed Analysis Applications
Q-GAIN is a Python package implementing ML classification, object detection, and physics-informed metrics for analyzing images of atomic BECs, demonstrated on MNIST, soliton detection, and vortex identification tasks.