System identification requires expert decisions on the identification method, incorporation of prior physical knowledge, and model validation. We propose ASPIRE, a framework for nonlinear system identification in which a large language model agent selects and executes the identification method. ASPIRE constructs closed-form, nonlinear static or dynamic models from measured data, optionally supplemented by a system description, the intended use of the model, and physical requirements expressed formally or in natural language. Each model includes its parameters, an estimation record, an interpretation of its terms, and an error evaluated on test data inaccessible to the agent. Formal physical requirements are verified independently. ASPIRE operates autonomously or interactively, allowing the agent to ask questions and the user to request further analyses and identification rounds. We evaluate ASPIRE on three measured systems: a mobile robot, a rotational system with dry friction, and a laboratory fermenter. Each system is tested with and without a description, in five runs per task. All 30 runs delivered valid models, at a cost of 0.96 to 3.38 US dollars per run. An assessment by the authors found that, for the 30 models recommended by the agent, one per run, the interpretation of the model and the documentation of its structure selection and parameter estimation fully satisfied 132 of 150 assessed items and partly satisfied 18. The most frequent discrepancy, found in nine models, concerned inaccurate or unsupported claims about model structure selection.

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