Forcing-informed resolvent analysis extracts data-consistent forcing and response modes for self-sustained flows by estimating input-output subspaces from nonlinear forcing snapshots.
Mezi´ c, Analysis of Fluid Flows via Spectral Properties of the Koopman Operator, Annual Review of Fluid Mechanics, vol
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Optimizing training data via a differentiable SCM yields climate emulators that outperform those trained on six standard ScenarioMIP pathways while using less data and isolating distinct forcing responses.
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.
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.
A theoretical framework establishing representer theorems, Sobolev approximation bounds, and spectral convergence for kernel-based learning of spatio-temporal dynamical systems using OV RKHS and Koopman approximations.
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Optimal scenario design for climate emulation
Optimizing training data via a differentiable SCM yields climate emulators that outperform those trained on six standard ScenarioMIP pathways while using less data and isolating distinct forcing responses.