From External Information to Forecast Adjustment: LLM-Based Constraint Modeling and Reflection Acceleration

In complex real-world systems, forecasts based solely on historical data often fail under non-stationary dynamics induced by external information, ranging from stochastic events to rule-based operational constraints. We propose a novel post-forecast adjustment framework that refines existing forecasts by converting unstructured external knowledge into explicit mathematical constraints using large language models (LLMs). Our approach utilizes an LLM-based agent to extract and structure external information, which is then translated into mathematical constraints by a fine-tuned LLM. Given a base forecast from any statistical or machine learning model, the adjusted forecast is derived by solving a convex optimization problem that projects the base prediction onto the feasible region defined by these constraints. We employ a reflection and memory mechanism for iterative refinement, and introduce a novel constraint selection strategy based on mutual information and intervention effect analysis to accelerate the reflection process. Empirical results show that our framework significantly improves forecasting accuracy over base methods, including those that integrate external information via LLMs, while offering superior interpretability compared to direct LLM-based approaches.