TT-PINN: A Tensor-Compressed Neural PDE Solver for Edge Computing

TL;DR

This paper introduces TT-PINN, a tensor-compressed neural network that enables efficient physics-informed neural network training on edge devices by significantly reducing parameters while maintaining accuracy.

Contribution

The paper proposes a novel tensor-train decomposition-based compression method for PINNs, facilitating their deployment on resource-constrained edge devices.

Findings

Achieves up to 15x parameter reduction in Helmholtz equation problems.

Outperforms original PINNs in accuracy with fewer parameters.

Enables practical edge computing for physics-informed neural networks.

Abstract

Physics-informed neural networks (PINNs) have been increasingly employed due to their capability of modeling complex physics systems. To achieve better expressiveness, increasingly larger network sizes are required in many problems. This has caused challenges when we need to train PINNs on edge devices with limited memory, computing and energy resources. To enable training PINNs on edge devices, this paper proposes an end-to-end compressed PINN based on Tensor-Train decomposition. In solving a Helmholtz equation, our proposed model significantly outperforms the original PINNs with few parameters and achieves satisfactory prediction with up to 15$\times$ overall parameter reduction.