DPNO: A Dual Path Architecture For Neural Operator

TL;DR

This paper introduces DPNO, a dual path neural operator architecture that enhances feature extraction and solution accuracy for PDEs, outperforming traditional models by over 30% in some cases.

Contribution

The paper proposes a novel dual path architecture for neural operators, improving their performance and versatility across various PDE problems.

Findings

Achieves over 30% relative improvement on standard PDE test cases.

Demonstrates versatility by applying to DeepONet and FNO architectures.

Enhances feature extraction and solution approximation capabilities.

Abstract

Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring composition of basic operator blocks to achieve better per-formance. The traditional way of composition is staking those blocks like feedforward neural networks, which may not be very economic considering parameter-efficiency tradeoff. In this pa-per, we propose a novel dual path architecture that significantly enhances the capabilities of basic neural operators. The basic operator block is organized in parallel two paths which are similar with ResNet and DenseNet. By introducing this parallel processing mechanism, our architecture shows a more powerful feature extraction and solution approximation ability compared with the original model. We demonstrate the effectiveness of our approach through extensive numerical experi-ments on a variety of PDE problems, including the Burgers' equation, Darcy Flow Equation and the 2d Navier-Stokes equation. The experimental results indicate that on certain standard test cas-es, our model achieves a relative improvement of over 30% compared to the basic model. We also apply this structure on two standard neural operators (DeepONet and FNO) selected from different paradigms, which suggests that the proposed architecture has excellent versatility and offering a promising direction for neural operator structure design.