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Mathematical formulas serve as the means of communication between humans andnature, encapsulating the operational laws governing natural phenomena. Theconcise formulation of these laws is a crucial objective in scientific researchand an important challenge for artificial intelligence (AI). While traditionalartificial neural networks (MLP) excel at data fitting, they often yielduninterpretable black box results that hinder our understanding of therelationship between variables x and predicted values y. Moreover, the fixednetwork architecture in MLP often gives rise to redundancy in both networkstructure and parameters. To address these issues, we propose MetaSymNet, anovel neural network that dynamically adjusts its structure in real-time,allowing for both expansion and contraction. This adaptive network employs thePANGU meta function as its activation function, which is a unique type capableof evolving into various basic functions during training to composemathematical formulas tailored to specific needs. We then evolve the neuralnetwork into a concise, interpretable mathematical expression. To evaluateMetaSymNet's performance, we compare it with four state-of-the-art symbolicregression algorithms across more than 10 public datasets comprising 222formulas. Our experimental results demonstrate that our algorithm outperformsothers consistently regardless of noise presence or absence. Furthermore, weassess MetaSymNet against MLP and SVM regarding their fitting ability andextrapolation capability, these are two essential aspects of machine learningalgorithms. The findings reveal that our algorithm excels in both areas.Finally, we compared MetaSymNet with MLP using iterative pruning in networkstructure complexity. The results show that MetaSymNet's network structurecomplexity is obviously less than MLP under the same goodness of fit.

MetaSymNet: A Dynamic Symbolic Regression Network Capable of Evolving into Arbitrary Formulations