Symbolic regression (SR) is a powerful technique for discovering the
underlying mathematical expressions from observed data. Inspired by the success
of deep learning, recent efforts have focused on two categories for SR methods.
One is using a neural network or genetic programming to search the expression
tree directly. Although this has shown promising results, the large search
space poses difficulties in learning constant factors and processing
high-dimensional problems. Another approach is leveraging a transformer-based
model training on synthetic data and offers advantages in inference speed.
However, this method is limited to fixed small numbers of dimensions and may
encounter inference problems when given data is out-of-distribution compared to
the synthetic data. In this work, we propose DySymNet, a novel neural-guided
Dynamic Symbolic Network for SR. Instead of searching for expressions within a
large search space, we explore DySymNet with various structures and optimize
them to identify expressions that better-fitting the data. With a topology
structure like neural networks, DySymNet not only tackles the challenge of
high-dimensional problems but also proves effective in optimizing constants.
Based on extensive numerical experiments using low-dimensional public standard
benchmarks and the well-known SRBench with more variables, our method achieves
state-of-the-art performance in terms of fitting accuracy and robustness to
noise.

我们提出了 DySymNet，这是一个新颖的神经引导的动态符号网络，用于符号回归。通过对各种结构进行优化，我们能够更好地识别与数据更匹配的表达式，在低维和高维问题中都能取得卓越的性能。