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Efficient Dilated Squeeze and Excitation Neural Operator for Differential Equations

Prajwal Chauhan, Salah Eddine Choutri, Saif Eddin Jabari

TL;DR

Efficient surrogates for PDEs are needed to accelerate science and engineering workflows, but existing transformer-based and global-operator models are often computationally heavy. The authors propose D-SENO, a lightweight, fully convolutional neural operator that combines dilated convolution blocks with squeeze-and-excitation channel attention to capture multiscale and long-range dependencies without relying on Fourier transforms or self-attention. Across airfoil, pipe, Darcy, and Navier–Stokes benchmarks, D-SENO achieves strong accuracy while delivering substantial speedups (up to 20x) over state-of-the-art baselines, with ablations confirming the critical role of SE blocks. The approach scales well on high-resolution grids and offers a practical, hardware-friendly PDE surrogate with avenues for extension to unstructured meshes and physics-informed priors.

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.

Efficient Dilated Squeeze and Excitation Neural Operator for Differential Equations

TL;DR

Efficient surrogates for PDEs are needed to accelerate science and engineering workflows, but existing transformer-based and global-operator models are often computationally heavy. The authors propose D-SENO, a lightweight, fully convolutional neural operator that combines dilated convolution blocks with squeeze-and-excitation channel attention to capture multiscale and long-range dependencies without relying on Fourier transforms or self-attention. Across airfoil, pipe, Darcy, and Navier–Stokes benchmarks, D-SENO achieves strong accuracy while delivering substantial speedups (up to 20x) over state-of-the-art baselines, with ablations confirming the critical role of SE blocks. The approach scales well on high-resolution grids and offers a practical, hardware-friendly PDE surrogate with avenues for extension to unstructured meshes and physics-informed priors.

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 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.
Paper Structure (32 sections, 6 equations, 8 figures, 15 tables)

This paper contains 32 sections, 6 equations, 8 figures, 15 tables.

Table of Contents

  1. Introduction
  2. Our Contribution
  3. Related Work
  4. Fourier Neural Operator (FNO).
  5. Convolutional Neural Operator.
  6. Dilated Convolution Neural Operator.
  7. Background
  8. Dilated Convolutions
  9. Squeeze-and-Excitation Blocks
  10. Squeeze.
  11. Excitation.
  12. Method
  13. Learning solution operator for PDEs
  14. D-SENO
  15. Experiments
  16. ...and 17 more sections

Figures (8)

  • Figure 1: D-SENO architecture
  • Figure 2: Top. Dilated Convolution for 3 dilation rates, Middle. Cumulative tap locations for dilation rates $1,2,3$ (left to right), Bottom Receptive field growth with propagation for dilation rates $1,2,3$, each applied twice (left to right)
  • Figure 3: Sample from the Airfoil dataset.
  • Figure 4: Sample from the Pipe dataset.
  • Figure 5: Sample from the Darcy dataset.
  • ...and 3 more figures