# Divergence of predictive model output as indication of phase transitions

## TL;DR

This paper proposes a novel method using divergence in predictive model outputs, like neural networks, to detect phase transitions in physical systems without prior phase information.

## Contribution

It introduces a model-based divergence approach for identifying phase boundaries applicable to systems with arbitrary parameter dimensions.

## Key findings

- Effective detection of phase transitions in Ising and Kuramoto-Hopf models.
- Method does not require prior knowledge of phases.
- Applicable to high-dimensional parameter spaces.

## Abstract

We introduce a new method to identify phase boundaries in physical systems. It is based on training a predictive model such as a neural network to infer a physical system's parameters from its state. The deviation of the inferred parameters from the underlying correct parameters will be most susceptible and diverge maximally in the vicinity of phase boundaries. Therefore, peaks in the divergence of the model's predictions are used as indication of phase transitions. Our method is applicable for phase diagrams of arbitrary parameter dimension and without prior information about the phases. Application to both the two-dimensional Ising model and the dissipative Kuramoto-Hopf model show promising results.