Liu, Jingyi; Li, Weijun; Yu, Lina; Wu, Min; Li, Wenqiang; Li, Yanjie; Hao, Meilan Source: SSRN, January 11, 2024;

Abstract:

This paper introduces MSR, a generative neural network-based framework that incorporates an automatic module learning feature, aiming to enhance the search accuracy of Symbolic Regression (SR). Unlike existing deep model-based SR approaches, MSR identifies valuable sub-structures named modules, which are utilized to construct the final solution. Modules are considered high-order knowledge and act as fundamental operators, expanding the search library of SR. The proposed algorithm enables self-learning or self-evolution of modules as part of the learning component. By incorporating variables or partial solutions as input arguments, MSR facilitates the formation of sophisticated, higher-order, and constructive sub-structures, thereby improving search accuracy. Specifically, we propose a module extraction strategy that generates modules hierarchically from the expression tree, along with a module update mechanism designed to effectively eliminate unnecessary modules while incorporating new useful ones. To validate the effectiveness of MSR, we conducted experiments on 60 SR problems. Through ablation studies, we analyze the impact of module utilization and the module update mechanism. The experimental results demonstrate that our method outperforms scenarios where modules are not utilized or random updates are applied. Furthermore, our approach exhibits higher accuracy in SR problems involving constants, surpassing some state-of-the-arts. Our code has been released at https://anonymous.4open.science/r/MSR.

？ 2024, The Authors. All rights reserved. (31 refs.)