Identifying Ising and percolation phase transitions based on KAN method
This addresses the challenge of phase transition identification in physics models, but it appears incremental as it applies an existing KAN method to new data (percolation and Ising models).
The paper tackled the problem of identifying critical points in percolation models using raw configurations, and the result showed that the Kolmogorov-Arnold Network (KAN) can predict these critical points and also achieve phase classification for models like the Ising model.
Modern machine learning, grounded in the Universal Approximation Theorem, has achieved significant success in the study of phase transitions in both equilibrium and non-equilibrium systems. However, identifying the critical points of percolation models using raw configurations remains a challenging and intriguing problem. This paper proposes the use of the Kolmogorov-Arnold Network, which is based on the Kolmogorov-Arnold Representation Theorem, to input raw configurations into a learning model. The results demonstrate that the KAN can indeed predict the critical points of percolation models. Further observation reveals that, apart from models associated with the density of occupied points, KAN is also capable of effectively achieving phase classification for models where the sole alteration pertains to the orientation of spins, resulting in an order parameter that manifests as an external magnetic flux, such as the Ising model.