Identifying phase transitions in physical systems with neural networks: a neural architecture search perspective

TL;DR

This work addresses identifying phase transitions in Ising-like physical systems by regressing the phase parameter $T$ from spin configurations using neural architecture search (NAS) to optimize multilayer perceptrons. It introduces neuron coverage metrics to study internal activation patterns and their relation to phases, finding that NC—especially its stability and heightened activation near the critical region—serves as a promising indicator of phase transitions. The authors demonstrate that a neuroevolutionary NAS framework can produce high-performing architectures with low mean squared error (MSE) on temperature predictions, while coverage metrics provide diagnostic insight into model behavior across temperatures. Overall, combining NAS with neuron-activation coverage offers a valuable approach for diagnosing and understanding phase transitions in physical systems, with potential extensions to more complex or quantum systems.

Abstract

The use of machine learning algorithms to investigate phase transitions in physical systems is a valuable way to better understand the characteristics of these systems. Neural networks have been used to extract information of phases and phase transitions directly from many-body configurations. However, one limitation of neural networks is that they require the definition of the model architecture and parameters previous to their application, and such determination is itself a difficult problem. In this paper, we investigate for the first time the relationship between the accuracy of neural networks for information of phases and the network configuration (that comprises the architecture and hyperparameters). We formulate the phase analysis as a regression task, address the question of generating data that reflects the different states of the physical system, and evaluate the performance of neural architecture search for this task. After obtaining the optimized architectures, we further implement smart data processing and analytics by means of neuron coverage metrics, assessing the capability of these metrics to estimate phase transitions. Our results identify the neuron coverage metric as promising for detecting phase transitions in physical systems.

Figures (7)

• Figure 1: Histogram of the Test MSE for over $95\%$ of architectures in the last population.
• Figure 2: Mean MSE of the best $30$ models as a function of the temperature.
• Figure 3: Standard deviation of MSE of the best $30$ models as a function of the temperature.
• Figure 4: Standard deviation of the NC metric for the different temperatures.
• Figure 5: Mean value of the NC metric for the different temperatures.