Early detection of global instability via a large language model

We present a novel application of Chronos – a foundation model based on a large-language-model architecture pretrained on public time-series sequences – for the early detection of global instability in a low-density jet. Global instability in this system emerges via a Hopf bifurcation, whose incipient signatures are challenging to detect. Conventional indicators (e.g. lag-1 autocorrelation) require ad-hoc tuning, while data-driven tools (e.g. neural networks) require extensive system-specific training data. Our approach appends a single hidden-layer regressor to a frozen Chronos-T5 model and trains this lightweight regression head to output a scalar estimate of the proximity to the Hopf point. Training is performed with short, scale-normalized time traces of the jet velocity, projected into the 768-dimensional token space of Chronos. Despite training solely on supercritical bifurcation data, the model successfully generalizes to subcritical cases as well. This capability arises from the token embeddings being drawn from the finite vocabulary dictionary of Chronos. By leveraging this pre-learned language of time-series evolution, a shallow downstream regressor can identify the early signs ("words") of global instability, even for previously unseen bifurcations.