arXiv:2602.17829v1 Announce Type: new Abstract: Inferring causal relations in timeseries data with delayed effects is a fundamental challenge, especially when the underlying system exhibits complex dynamics that cannot be captured by simple functional mappings. Traditional approaches often fail to produce generalized and interpretable explanations, as multiple distinct input trajectories may yield nearly indistinguishable outputs. In this work, we present ruleXplain, a framework that leverages Large Language Models (LLMs) to extract formal explanations for input-output relations in simulation-driven dynamical systems. Our method introduces a constrained symbolic rule language with temporal operators and delay semantics, enabling LLMs to generate verifiable causal rules through structured prompting. ruleXplain relies on the availability of a principled model (e.g., a simulator) that maps multivariate input time series to output time series. Within ruleXplain, the simulator is used to generate diverse counterfactual input trajectories that yield similar target output, serving as candidate explanations. Such counterfactual inputs are clustered and provided as context to the LLM, which is tasked with the generation of symbolic rules encoding the joint temporal trends responsible for the patterns observable in the output times series. A closed-loop refinement process ensures rule consistency and semantic validity. We validate the framework using the PySIRTEM epidemic simulator, mapping testing rate inputs to daily infection counts; and the EnergyPlus building energy simulator, observing temperature and solar irradiance inputs to electricity needs. For validation, we perform three classes of experiments: (1) the efficacy of the ruleset through input reconstruction; (2) ablation studies evaluating the causal encoding of the ruleset; and (3) generalization tests of the extracted rules across unseen output trends with varying phase dynamics.