Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics

We employ physics-informed neural networks (PINNs) to solve fundamental Dyson-Schwinger integral equations in the theory of quantum electrodynamics (QED) in Euclidean space. Our approach uses neural networks to approximate the fermion wave function renormalization, dynamical mass function, and photon propagator. By integrating the Dyson-Schwinger equations into the loss function, the networks learn and predict solutions over a range of momenta and ultraviolet cutoff values. This method can be extended to other quantum field theories (QFTs), potentially paving the way for forefront applications of machine learning within high-level theoretical physics.

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

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.