MetaSymNet: A Dynamic Symbolic Regression Network Capable of Evolving
  into Arbitrary Formulations
Yanjie Li Weijun Li Lina Yu Min Wu Jinyi Liu Wenqiang Li Meilan Hao Shu Wei Yusong Deng
Mathematical formulas serve as the means of communication between humans and
nature, encapsulating the operational laws governing natural phenomena. The
concise formulation of these laws is a crucial objective in scientific research
and an important challenge for artificial intelligence (AI). While traditional
artificial neural networks (MLP) excel at data fitting, they often yield
uninterpretable black box results that hinder our understanding of the
relationship between variables x and predicted values y. Moreover, the fixed
network architecture in MLP often gives rise to redundancy in both network
structure and parameters. To address these issues, we propose MetaSymNet, a
novel neural network that dynamically adjusts its structure in real-time,
allowing for both expansion and contraction. This adaptive network employs the
PANGU meta function as its activation function, which is a unique type capable
of evolving into various basic functions during training to compose
mathematical formulas tailored to specific needs. We then evolve the neural
network into a concise, interpretable mathematical expression. To evaluate
MetaSymNet's performance, we compare it with four state-of-the-art symbolic
regression algorithms across more than 10 public datasets comprising 222
formulas. Our experimental results demonstrate that our algorithm outperforms
others consistently regardless of noise presence or absence. Furthermore, we
assess MetaSymNet against MLP and SVM regarding their fitting ability and
extrapolation capability, these are two essential aspects of machine learning
algorithms. The findings reveal that our algorithm excels in both areas.
Finally, we compared MetaSymNet with MLP using iterative pruning in network
structure complexity. The results show that MetaSymNet's network structure
complexity is obviously less than MLP under the same goodness of fit.