Efficient Dilated Squeeze and Excitation Neural Operator for Differential Equations

Prajwal Chauhan, Salah Eddine Choutri, Saif Jabari

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 $\approx 20\times$ 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.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

## Changes since the last submission (revised manuscript)

### 1) Clarifications and text fixes
- Corrected the typo in the Discussion (p. 8): FNO+ outperforms FNO on **four** datasets (including Navier–Stokes).
- Fixed formatting and notation issues (e.g., DNCO not bold; wrote $u = G(a)$ instead of $G(a)=u$).

### 2) Added/expanded method details
- Expanded Section 3 to explain where channels are reduced/restored (explicitly describing the squeeze-and-excitation block and where it is applied).
- Clarified that “adaptivity” refers to SE-based channel recalibration, not dilation rates (Section 4.2, first paragraph).
- Added brief description of selection of dilation rates in appendix in section "A.1.3 Dilation rate impact".
- Added subsection describing the improvements to the original FNO in the appendix.

### 3) New experiments / additional results
- Added parameter-matched comparisons with and without SE-blocks (Appendix, Table 5,7,9 and 11).

### 4) Limitations / scope
- Added a dedicated limitations subsection under section 7.

### 5) Reproducibility
- Pointed readers to hyperparameter/configuration tables in the main manuscript (Tables 3–4).
- Added/clarified dataset links in the Appendix in sub-section A.1, first paragraph.

## Changes since the last submission (Camera ready manuscript)

### 1) Codebase:
- Added link to the code for D-SENO and FNO$^+$.

### 2) Acknowledgement:
- Added an acknowledgement section at the end of main body.

Code: https://github.com/pj1911/Efficient-Dilated-Squeeze-and-Excitation-Neural-Operator-for-Differential-Equations

Assigned Action Editor: ~Francesco_Locatello1

Submission Number: 5991