A practical input-to-state stability certificate for Koopman learning control is derived, separating prediction residuals from selected-channel margins and projection residuals.
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Spectral analysis of nonlinear flows,
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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.
WGFINNs use weak-form loss functions with GENERIC structure preservation to recover governing equations more accurately from noisy observations than prior strong-form GFINNs.
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.
Establishes a standardized Common Task Framework with three multi-scale seismic wavefield datasets and metrics to enable rigorous head-to-head evaluation of ML methods for reconstruction, forecasting, and generalization.
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.
A tensor train method computes the Koopman generator via operator logarithm while preserving low-rank structure for scalable identification of high-dimensional nonlinear dynamics.
Koopman autoencoders with attention-free latent memory and online change-point re-encoding reduce long-horizon error on Duffing, Repressilator, and IRMA benchmarks while keeping low latency.
Two new DOD-based reduced-order models (DOD-DL-ROM and DOD+DFNN) are introduced for hybrid-type parabolic PDEs, with rigorous error bounds linking performance to optimal map regularity and conditions for outperforming POD methods.
citing papers explorer
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Input-to-State Stability Certification via Projection Residuals for Koopman Learning Control of Nonlinear Repetitive Systems
A practical input-to-state stability certificate for Koopman learning control is derived, separating prediction residuals from selected-channel margins and projection residuals.
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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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WGFINNs: Weak formulation-based GENERIC formalism informed neural networks
WGFINNs use weak-form loss functions with GENERIC structure preservation to recover governing equations more accurately from noisy observations than prior strong-form GFINNs.
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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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The Seismic Wavefield Common Task Framework
Establishes a standardized Common Task Framework with three multi-scale seismic wavefield datasets and metrics to enable rigorous head-to-head evaluation of ML methods for reconstruction, forecasting, and generalization.
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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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Tensor-based computation of the Koopman generator via operator logarithm
A tensor train method computes the Koopman generator via operator logarithm while preserving low-rank structure for scalable identification of high-dimensional nonlinear dynamics.
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Learning the Koopman Operator using Attention Free Transformers
Koopman autoencoders with attention-free latent memory and online change-point re-encoding reduce long-horizon error on Duffing, Repressilator, and IRMA benchmarks while keeping low latency.
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A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications
Two new DOD-based reduced-order models (DOD-DL-ROM and DOD+DFNN) are introduced for hybrid-type parabolic PDEs, with rigorous error bounds linking performance to optimal map regularity and conditions for outperforming POD methods.