arXiv:2610.31318v1 Announce Type: new Abstract: Nonlinear system identification often requires costly experimental campaigns and separate model fitting for each different instance (target system) of a given system family. To reduce this burden, meta-learning approaches reuse information acquired across related systems. In particular, in-context meta-learning enables zero-shot prediction from a brief target system context (i.e., a short input-output trajectory), but generally yields large black-box sequence predictors without exposing an explicit state space model. Conversely, compact structured state space models are suitable for simulation, estimation, and control, but are usually fitted or adapted separately for each target system. To bridge this gap, we introduce a transfer meta-learning extension of state space autoencoders. The method reuses a pretrained encoder, whose weights remain fixed, to extract a compact representation of the target system from its context. An affine parameterization maps this representation to the parameters of a compact neural state space model without target-specific adaptation; the resulting model contains orders of magnitude fewer parameters than the reference in-context predictors from the literature. We evaluate zero-shot prediction and simulation performance on held-out system instances from Buck-Boost converter and Bouc-Wen oscillator system families, comparing performance against individually fitted baseline models.