Effective Field Neural Network
This work addresses the challenge of encoding domain knowledge into machine learning for physicists dealing with many-body problems, representing an incremental improvement with specific gains.
The authors tackled the curse of dimensionality in many-body physics problems by proposing effective field neural networks (EFNNs), which significantly outperformed fully-connected deep neural networks and effective models in case studies, with relative errors decreasing when applied to larger systems without retraining.
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.