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We used machine learning models to predict nucleation in the Ising model. Convolutional neural networks showed improved accuracy near critical points, outperforming logistic regression for nucleation prediction.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Machine Learning

Background:

  • The two-dimensional Ising model is a fundamental model in statistical mechanics.
  • Nucleation phenomena are critical for understanding phase transitions.
  • Predicting nucleation probability is essential for various physical systems.

Purpose of the Study:

  • To evaluate the effectiveness of machine learning models, specifically convolutional neural networks (CNNs) and logistic regression, in predicting nucleation probability.
  • To compare the performance of these models in the context of the two-dimensional Ising model, particularly near critical points.

Main Methods:

  • Development and application of a convolutional neural network (CNN).
  • Implementation of two logistic regression models.
  • Testing models on the two-dimensional Ising model with varying interaction ranges (nearest-neighbor and long-range).
  • Utilizing occlusion analysis to understand model behavior.

Main Results:

  • All three models successfully predicted nucleation probability for the nearest-neighbor Ising model.
  • The CNN demonstrated superior performance compared to logistic regression models near the spinodal of the long-range Ising model.
  • Model prediction accuracy decreased as simulations approached the spinodal, attributed to diminishing density differences between nucleating droplets and the background.

Conclusions:

  • Machine learning models, particularly CNNs, can effectively predict nucleation probability in statistical physics models.
  • Predictability decreases near critical points, a phenomenon observed across different models and methods.
  • The findings highlight the potential of AI in understanding complex physical phenomena like phase transitions.