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.
翻译:复杂的自然系统的运作机制往往遵守简洁和深刻的局部差异方程式(PDEs) 数据直接开采方程式的方法称为PDE发现法,这种方法揭示了连贯的物理法则,便利了我们与自然界的适应性互动。在本文件中,建议加强深层强化学习框架,以发现具有象征性的、简洁的开放式PDE,而事先知识甚少。特别是,基于一个基本操作者和操作者象征图书馆,设计了一个结构能觉察到的经常性神经网络代理物,与稀薄的回归法无缝结合,以产生简洁和开放的PDE表达法。所有生成的PDE都是通过精心设计的奖励功能进行评估的,其方法是平衡数据与相容和相近,并以基于模型的强化学习有效方式加以更新。制定定制的限制和条例,以保障PDE在物理和数学方面合理性。实验表明,我们的框架能够开采若干动态系统的公开式方程式方程式,即使有复合方程式条件、分形结构以及高序衍生物,而且效率极佳。不需要事先的知识,这一方法在非常复杂的情况下,在非常复杂的情况下显示发现知识的可能性。</s>