Efficient Dilated Squeeze and Excitation Neural Operator for Differential Equations
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| Format: | Preprint |
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2026
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| author | Chauhan, Prajwal Choutri, Salah Eddine Jabari, Saif Eddin |
| author_facet | Chauhan, Prajwal Choutri, Salah Eddine Jabari, Saif Eddin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_17407 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient Dilated Squeeze and Excitation Neural Operator for Differential Equations Chauhan, Prajwal Choutri, Salah Eddine Jabari, Saif Eddin Machine Learning 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. |
| title | Efficient Dilated Squeeze and Excitation Neural Operator for Differential Equations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.17407 |