# Machine learning topological defect formation

## TL;DR

This paper explores how machine learning, specifically Recurrent Neural Networks, can predict the final configuration of topological defects during phase transitions by analyzing early-time order parameter evolution, aligning with Kibble-Zurek scaling.

## Contribution

It introduces a novel approach using ML to predict defect formation during phase transitions based on early dynamics, extending KZM insights.

## Key findings

- ML predictions follow KZM power law scaling
- Recurrent Neural Networks successfully predict defect configurations
- Early-time order parameter data suffices for accurate predictions

## Abstract

According to the Kibble-Zurek mechanism (KZM), the density of topological defects created during a second-order phase transition is determined by the correlation length at the freeze-out time. This suggests that the final configuration of topological defects in such a transition is largely established during the impulse regime, soon after the critical point is traversed. Motivated by this, we conjecture that machine learning (ML) can predict the final configuration of topological defects based on the time evolution of the order parameter over a short interval in the vicinity of the critical point, well before the order parameter settles into the emerging new minima resulting from spontaneous symmetry breaking. Furthermore, we show that the predictability of ML also follows the power law scaling dictated by KZM. We demonstrate these using a Recurrent Neural Network.