Effective Field Neural Network

Effective Field Neural Network Xi Liu, 1 Yujun Zhao, 1 Chun Yu Wan, 1 Yang Zhang, 2, 3 and Junwei Liu 1, 1 Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China 2 Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA 3 Min H. Kao Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA (Dated: February 26, 2025) In recent years, with the rapid development of machine learning, physicists have been exploring its new applications in solving or alleviating the curse of dimensionality in many-body problems. In order to accurately reflect the underlying physics of the problem, domain knowledge must be encoded into the machine learning algorithms. In this work, inspired by field theory, we propose a new set of machine learning models called effective field neural networks (EFNNs) that can automatically and efficiently capture important many-body interactions through multiple self-refining processes. Taking the classical 3-spin infinite-range model and the quantum double exchange model as case studies, we explicitly demonstrate that EFNNs significantly outperform fully-connected deep neural networks (DNNs) and the effective model. Furthermore, with the help of convolution operations, the EFNNs learned in a small system can be seamlessly used in a larger system without additional training and the relative errors even decrease, which further demonstrates the efficacy of EFNNs in representing core physical behaviors.