LogicGate: Adaptive Rule-Based Modeling of Exogenous Effects for Time Series Forecasting

Time series forecasting is pivotal in many critical domains such as weather prediction, energy management, and disease monitoring. To accurately model temporal dynamics, an increasing number of researchers are integrating exogenous variables (e.g., structured domain knowledge, etc.), into conventional data-driven methods, enabling models to learn generalizable principles beyond statistical correlations. However, these approaches remain limited by two core design flaws: (1) static knowledge bases that cannot adapt to evolving data environments, and (2) shallow fusion mechanisms that fail to capture the complex, context-dependent relationships between exogenous drivers and target variables. To address these challenges, we propose LogicGate, an adaptive forecasting framework that enables the co-evolution of the prediction model and its rule-guided knowledge base. When modeling the impact of exogenous features to the target time series variables, LogicGate employs a Dynamic Rule Filter to adaptively select context-relevant knowledge, a Cross-modal Fusion Module to inject rule semantics through rule-guided attention, and a Dual-Track Self-Optimization Framework that leverages large language models (LLMs) to autonomously refine its knowledge base. Extensive experiments on multiple real-world benchmarks demonstrate that LogicGate consistently outperforms state-of-the-art baselines, validating its effectiveness in integrating and evolving domain knowledge for time series forecasting. Code are available at https://github.com/Excelsiorise/Logicgate.git .