Smallest neural network to learn the Ising criticality.

Area of Science:

• Physics
• Computational Science
• Machine Learning

Background:

• Artificial neural networks (ANNs) model system behavior via data-driven training.
• Minimizing ANN complexity without performance loss is crucial for understanding their function.
• The Ising model is a fundamental model in statistical mechanics for studying phase transitions.

Purpose of the Study:

• To investigate the minimum complexity of ANNs required for accurate phase transition prediction in the Ising model.
• To determine if ANNs can reveal underlying physical principles during training.
• To explore the generalization capabilities of trained ANNs across different lattice geometries.

Main Methods:

• Training feed-forward artificial neural networks on Ising model data.
• Analyzing network parameters and performance to assess complexity and accuracy.
• Evaluating the network's ability to predict critical temperature and learn scaling dimensions.

Main Results:

• A simple ANN with only two hidden neurons accurately predicts the critical temperature of the Ising model.
• The trained networks demonstrate learning of the order parameter's scaling dimension.
• The ANNs exhibit universality, generalizing across different lattice geometries with the same criticality.

Conclusions:

• Minimal neural network architectures can effectively capture complex physical phenomena like phase transitions.
• Machine learning models can implicitly learn fundamental physical concepts like universality.
• This work provides insights into interpretable machine learning for physical systems.