In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

翻译：在符号回归中，目标是找到一种能准确拟合实验数据的解析表达式，同时最小化运算符、变量和常量等数学符号的使用。然而，可能表达式的组合空间使得传统进化算法难以在合理时间内找到正确表达式。为解决这一问题，研究者开发了神经符号回归（NSR）算法，该算法能快速识别数据中的模式并生成解析表达式。然而，现有方法缺乏整合用户定义的先验知识的能力，而这在自然科学和工程领域常常是必要的。为克服这一局限，我们提出了一种新型神经符号回归方法——带假设的神经符号回归（NSRwH），它能够将关于真实表达式预期结构的显式假设融入预测过程。实验表明，所提出的条件深度学习模型在精度上优于非条件对应模型，同时还能对预测表达式的结构进行控制。