Extending machine learning classification capabilities with histogram reweighting.

Area of Science:

• Computational Physics
• Machine Learning Applications
• Statistical Mechanics

Background:

• Extrapolating machine learning (ML) model predictions across continuous parameter ranges is challenging.
• Traditional methods may struggle with physical systems lacking clear order parameters or where direct sampling is difficult.

Purpose of the Study:

• To propose and validate a novel method combining Monte Carlo histogram reweighting with ML.
• To enable extrapolation of ML model predictions in statistical physics systems.
• To improve precision measurements from ML in challenging physical scenarios.

Main Methods:

• Treating convolutional neural network (CNN) outputs as statistical observables.
• Applying Monte Carlo histogram reweighting to extrapolate CNN predictions.
• Utilizing the two-dimensional Ising model phase transition for demonstration.

Main Results:

• Interpreting CNN output as an order parameter revealed connections to known system observables.
• Finite-size scaling analysis based on CNN-derived quantities yielded accurate critical exponents and temperature.
• Demonstrated successful extrapolation of ML predictions over continuous parameter ranges.

Conclusions:

• The proposed method enhances the predictive power of ML in statistical physics.
• It offers a pathway to precision measurements in systems where direct sampling is infeasible.
• This approach is particularly valuable for systems lacking a traditional order parameter.