DISCOVER: Deep identification of symbolically concise open-form PDEs via enhanced reinforcement-learning
This work addresses the challenge of knowledge discovery in complex natural systems for researchers in physics and engineering, though it appears incremental as it builds on existing PDE discovery methods by integrating reinforcement learning with sparse regression.
The authors tackled the problem of discovering concise partial differential equations (PDEs) from data with minimal prior knowledge, proposing an enhanced deep reinforcement-learning framework that successfully mines open-form governing equations for dynamic systems, including those with compound terms and high-order derivatives, with excellent efficiency.
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws and facilitates our adaptive interaction with the natural world. In this paper, an enhanced deep reinforcement-learning framework is proposed to uncover symbolically concise open-form PDEs with little prior knowledge. Particularly, based on a symbol library of basic operators and operands, a structure-aware recurrent neural network agent is designed and seamlessly combined with the sparse regression method to generate concise and open-form PDE expressions. All of the generated PDEs are evaluated by a meticulously designed reward function by balancing fitness to data and parsimony, and updated by the model-based reinforcement learning in an efficient way. Customized constraints and regulations are formulated to guarantee the rationality of PDEs in terms of physics and mathematics. The experiments demonstrate that our framework is capable of mining open-form governing equations of several dynamic systems, even with compound equation terms, fractional structure, and high-order derivatives, with excellent efficiency. Without the need for prior knowledge, this method shows great potential for knowledge discovery in more complicated circumstances with exceptional efficiency and scalability.