Recurrent Domain Incremental Adaptation of Time-Series Foundation Models

Pretrained Time-Series Foundation Models (TSFMs) provide strong representations for downstream classification tasks. Yet adapting a TSFM under changing operating conditions remains challenging. A model must improve on each newly observed condition without sacrificing conditions it has already learned, often from only a small labeled calibration set and without knowing the operating condition at inference time. We find that this difficulty has an important geometric structure. Under an operating-condition shift, the embedding space of a TSFM does not move uniformly: some local regions change substantially, while others remain nearly unchanged. Consequently, a global adaptation can unnecessarily move embeddings that were already correctly classified. To address this, we propose the novel PACT (Piecewise Adaptation via Chart Transport). PACT partitions the frozen source embedding space into local charts and learns lightweight residual transports for the regions affected by each new condition. An explicit identity path is always retained, and a learned gate softly selects among the identity and accumulated transports for each input. The pretrained TSFM encoder, classifier head, and previously learned transports remain fixed. With only 5% labeled calibration data per arriving condition and no condition identity at test time, PACT maintains above 0.95 average macro-F1 across a four-condition bearing-fault stream. Under homogeneous tasks and label spaces, similar retention-adaptation behavior is observed across public benchmarks.