In-Context Learning for System Identification: Probabilistic Formulation, Long-Sequence Handling, and Benchmark Validation

arXiv:2610.13411v1 Announce Type: new Abstract: Traditional system identification typically involves two steps: initially, training data is processed to estimate a model of the system of interest; then, the model is used to predict outputs for new input queries. In contrast, recent in-context learning approaches learn a meta model that maps directly from training data and query inputs to outputs in a zero-shot fashion, bypassing explicit model estimation. This approach leverages a meta model trained offline, on large sets of synthetically generated data, to emulate the behavior of a system identification algorithm. In this work, we advance this meta-learning framework for system identification in three directions. First, we develop a unified probabilistic meta-identification architecture that combines a Transformer-based encoder-decoder with tailored mechanisms for handling long training sequences, enabling calibrated predictions over long horizons. Second, we show how a pre-trained meta model can act as an uncertainty-aware synthetic data generator for classical system identification, providing task-specific data that regularize parametric models when real data are scarce. Third, we systematically evaluate the framework on standard nonlinear system identification benchmarks and on a challenging out-of-distribution scenario, demonstrating competitive accuracy with state-of-the-art methods and strong generalization, including cases where input-only adaptation is sufficient to handle significant distribution shifts.

Abstract:Traditional system identification typically involves two steps: initially, training data is processed to estimate a model of the system of interest; then, the model is used to predict outputs for new input queries. In contrast, recent in-context learning approaches learn a meta model that maps directly from training data and query inputs to outputs in a zero-shot fashion, bypassing explicit model estimation. This approach leverages a meta model trained offline, on large sets of synthetically generated data, to emulate the behavior of a system identification algorithm. In this work, we advance this meta-learning framework for system identification in three directions. First, we develop a unified probabilistic meta-identification architecture that combines a Transformer-based encoder-decoder with tailored mechanisms for handling long training sequences, enabling calibrated predictions over long horizons. Second, we show how a pre-trained meta model can act as an uncertainty-aware synthetic data generator for classical system identification, providing task-specific data that regularize parametric models when real data are scarce. Third, we systematically evaluate the framework on standard nonlinear system identification benchmarks and on a challenging out-of-distribution scenario, demonstrating competitive accuracy with state-of-the-art methods and strong generalization, including cases where input-only adaptation is sufficient to handle significant distribution shifts.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Systems and Control (eess.SY)

arXiv:2610.13411 [cs.LG]

(or arXiv:2610.13411v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.13411 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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In-Context Learning for System Identification: Probabilistic Formulation, Long-Sequence Handling, and Benchmark Validation

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