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,目标是找到一种解析表达式,用最少的数学符号(如算子、变量和常数)来准确拟合实验数据。然而,可能的表达式组合空间使传统进化算法在合理的时间内难以找到正确的表达式。为解决这个问题,已经开发了神经符号回归(NSR)算法,它可以快速识别数据中的模式并生成解析表达式。然而,在当前形式下,这些方法缺乏将用户定义的先验知识纳入预测过程中的能力,而在自然科学和工程领域,这种先验知识经常是必需的。为了克服这个限制,我们提出了一种新的神经符号回归方法,称为带假设的神经符号回归(NSRwH),它使基于对实际表达式预期结构的假设能够被纳入预测过程。我们的实验表明,所提出的有条件深度学习模型在准确性方面优于其无条件的对照组,并提供对预测表达式结构的控制。