NAS-PINNv2: Improved neural architecture search framework for physics-informed neural networks in low-temperature plasma simulation

TL;DR

This paper introduces NAS-PINNv2, an improved neural architecture search framework tailored for physics-informed neural networks in low-temperature plasma simulations, addressing previous limitations with complex equations.

Contribution

The paper presents NAS-PINNv2, a novel architecture search method that effectively handles complex plasma equations, incorporating sigmoid-based weights and new loss terms for better neural network design.

Findings

NAS-PINNv2 outperforms previous methods in complex plasma simulations.

Larger neural networks are not always better for PINNs.

Flexible architectures with multiple neuron counts improve performance.

Abstract

Limited by the operation and measurement conditions, numerical simulation is often the only feasible approach for studying plasma behavior and mechanisms. Although artificial intelligence methods, especially physics-informed neural network (PINN), have been widely applied in plasma simulation, the design of the neural network structures still largely relies on the experience of researchers. Meanwhile, existing neural architecture search methods tailored for PINN have encountered failures when dealing with complex plasma governing equations characterized by variable coefficients and strong nonlinearity. Therefore, we propose an improved neural architecture search-guided method, namely NAS-PINNv2, to address the limitations of existing methods. By analyzing the causes of failure, the sigmoid function is applied to calculate the architecture-related weights, and a new loss term is introduced. The performance of NAS-PINNv2 is verified in several numerical experiments including the Elenbaas-Heller equation without and with radial velocity, the drift-diffusion-Poisson equation and the Boltzmann equation. The results again emphasize that larger neural networks do not necessarily perform better, and the discovered neural architecture with multiple neuron numbers in a single hidden layer imply a more flexible and sophisticated design rule for fully connected networks.