Weak-form Extended Dynamic Mode Decomposition
arXiv:2607.25950
2026
Dynamics
1 ideas extracted · analyzed Aug 31, 2026
What the math gives to ML
The paper develops a weak-form Extended Dynamic Mode Decomposition method that avoids estimating noisy time derivatives directly. Integration by parts transfers differentiation from observed trajectories to smooth test functions, producing a Koopman-generator regression with controllable noise amplification. This mechanism can be transferred to neural state-space models by learning an encoder whose latent coordinates obey weakly identified linear dynamics. The key falsifiable prediction is that weak residual variance is determined by the squared derivative weights of the test functions and avoids the inverse-sampling-step noise blow-up of finite differences.
Ideas from this paper
✗ Failed on benchmark
2026
Replace noisy pointwise derivative matching in a neural state-space model with a weak-form Koopman-generator residual. An encoder maps observations to latent observables, while a learned matrix generator propagates those observables. Integration by parts removes the need to differentiate noisy trajectories and provides a controllable noise-averaging mechanism.
Useful8/10
Difficulty5/10
Novelty7/10