<p>Extracting basic behavioral patterns or control equations from data has significant prospects for enhancing our understanding and utilization of physical systems in science and engineering. However, traditional methods for extracting these control equations often require a pre-obtained library containing candidate function terms, which is typically large and complex. Additionally, the collected data often contains noise, limiting the effectiveness of equation learning. To address this challenge, this paper proposes a reinforcement learning and genetic algorithm-based knowledge-guided dual-layer optimization structure algorithm (RLKGGA) for equation discovery, which combines reinforcement learning and genetic algorithms to identify partial differential equations (PDEs) thoroughly. Specifically, the Savitzky–Golay filter preprocesses the data, while the long short-term memory (LSTM) proxy generates a predetermined traversal sequence of the binary tree, facilitating the derivation of each PDE expression. Subsequently, under the guidance of an adaptive selection strategy, the obtained individuals are updated using a genetic algorithm to ensure the algorithm’s efficiency. Furthermore, a knowledge-guided double-layer optimization structure is proposed to aid in discovering complex partial differential equations. Manual constraints are utilized to eliminate unreasonable equations. Additionally, the LSTM is optimized through reinforcement learning, with a reward function designed to allocate rewards to each expression. Finally, the effectiveness of the method was experimentally verified, indicating that RLKGGA can proficiently identify control equations in various systems, including PDEs with complex forms and high-order derivatives. It also demonstrates robust performance in handling noisy data.</p>