MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shifts

What the math gives to ML

The paper's transferable core is the combination of Koopman linearization and conjugate Bayesian regression: a nonlinear encoder maps observations into a latent space where dynamics are linear, while a Matrix Normal-Inverse Wishart prior can be updated in closed form from a short trajectory segment. This gives a computationally cheap alternative to repeatedly adapting all neural-network weights under distribution shift, and it produces calibrated epistemic plus aleatoric uncertainty for multi-step rollouts. The most practical neural-network transfer is a meta-learned latent linear dynamics head whose prior is adapted online by sufficient-statistic updates, with the encoder trained across tasks.