Machine learning for structure-property mapping of Ising models: Scalability and limitations.

Area of Science:

• Computational Physics
• Machine Learning
• Condensed Matter Physics

Background:

• Machine learning (ML) offers computational efficiency for complex systems.
• Scalability and transferability are key challenges in applying ML to physics.
• Linear-scaling computation often relies on divide-and-conquer strategies based on property locality.

Purpose of the Study:

• To develop a scalable ML framework for predicting intensive properties and classifying phases of Ising models.
• To investigate the relationship between ML model performance and system characteristics like correlation length.
• To establish a method for predicting large-scale system properties by averaging smaller block predictions.

Main Methods:

• Developed an ML model based on the locality assumption for predicting intensive properties of finite-size blocks.
• Applied a divide-and-conquer approach by partitioning systems into subdomains.
• Averaged ML model predictions from randomly sampled blocks to estimate properties of large-scale systems.
• Analyzed the impact of ML block size relative to the characteristic length scale and correlation length.

Main Results:

• Demonstrated a scalable ML framework applicable to Ising models.
• Showed that ML prediction accuracy is limited by the system's characteristic length scale, particularly near critical points.
• Identified a scaling relation between prediction accuracy and the ratio of ML block size to spin-spin correlation length.

Conclusions:

• The proposed ML framework provides a scalable approach for property prediction and phase classification in many-body systems.
• The effectiveness of the ML approach is contingent on the block size being larger than the system's correlation length.
• The findings have implications for applying ML to diverse condensed-matter systems and understanding phase transitions.