Efficient Dilated Squeeze and Excitation Neural Operator for Differential Equations

TL;DR

The paper introduces D-SENO, a lightweight neural operator combining dilated convolutions and squeeze-and-excitation modules, achieving faster training and comparable or better accuracy for solving various PDEs.

Contribution

It presents a novel neural operator architecture that efficiently captures long-range dependencies and channel-wise features, outperforming existing models in speed and accuracy.

Findings

Training speed up to 20x faster than transformer-based models

Achieves comparable or superior accuracy on multiple PDE benchmarks

Ablation studies confirm the importance of SE modules

Abstract

Fast and accurate surrogates for physics-driven partial differential equations (PDEs) are essential in fields such as aerodynamics, porous media design, and flow control. However, many transformer-based models and existing neural operators remain parameter-heavy, resulting in costly training and sluggish deployment. We propose D-SENO (Dilated Squeeze-Excitation Neural Operator), a lightweight operator learning framework for efficiently solving a wide range of PDEs, including airfoil potential flow, Darcy flow in porous media, pipe Poiseuille flow, and incompressible Navier Stokes vortical fields. D-SENO combines dilated convolution (DC) blocks with squeeze-and-excitation (SE) modules to jointly capture wide receptive fields and dynamics alongside channel-wise attention, enabling both accurate and efficient PDE inference. Carefully chosen dilation rates allow the receptive field to focus on critical regions, effectively modeling long-range physical dependencies. Meanwhile, the SE modules adaptively recalibrate feature channels to emphasize dynamically relevant scales. Our model achieves training speed of up to approximately $20\times$ faster than standard transformer-based models and neural operators, while also surpassing (or matching) them in accuracy across multiple PDE benchmarks. Ablation studies show that removing the SE modules leads to a slight drop in performance.