SPUS: A Lightweight and Parameter-Efficient Foundation Model for PDEs

Fuente: arXiv
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Auteurs principaux: Siddik, Abu Bucker, Oyen, Diane, Most, Alexander, Kucer, Michal, Biswas, Ayan
Format: Preprint
Publié: 2025
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author Siddik, Abu Bucker
Oyen, Diane
Most, Alexander
Kucer, Michal
Biswas, Ayan
author_facet Siddik, Abu Bucker
Oyen, Diane
Most, Alexander
Kucer, Michal
Biswas, Ayan
contents We introduce Small PDE U-Net Solver (SPUS), a compact and efficient foundation model (FM) designed as a unified neural operator for solving a wide range of partial differential equations (PDEs). Unlike existing state-of-the-art PDE FMs-primarily based on large complex transformer architectures with high computational and parameter overhead-SPUS leverages a lightweight residual U-Net-based architecture that has been largely underexplored as a foundation model architecture in this domain. To enable effective learning in this minimalist framework, we utilize a simple yet powerful auto-regressive pretraining strategy which closely replicates the behavior of numerical solvers to learn the underlying physics. SPUS is pretrained on a diverse set of fluid dynamics PDEs and evaluated across 6 challenging unseen downstream PDEs spanning various physical systems. Experimental results demonstrate that SPUS using residual U-Net based architecture achieves state-of-the-art generalization on these downstream tasks while requiring significantly fewer parameters and minimal fine-tuning data, highlighting its potential as a highly parameter-efficient FM for solving diverse PDE systems.
format Preprint
id arxiv_https___arxiv_org_abs_2510_01370
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle SPUS: A Lightweight and Parameter-Efficient Foundation Model for PDEs
Siddik, Abu Bucker
Oyen, Diane
Most, Alexander
Kucer, Michal
Biswas, Ayan
Computer Vision and Pattern Recognition
Artificial Intelligence
Machine Learning
Computational Physics
We introduce Small PDE U-Net Solver (SPUS), a compact and efficient foundation model (FM) designed as a unified neural operator for solving a wide range of partial differential equations (PDEs). Unlike existing state-of-the-art PDE FMs-primarily based on large complex transformer architectures with high computational and parameter overhead-SPUS leverages a lightweight residual U-Net-based architecture that has been largely underexplored as a foundation model architecture in this domain. To enable effective learning in this minimalist framework, we utilize a simple yet powerful auto-regressive pretraining strategy which closely replicates the behavior of numerical solvers to learn the underlying physics. SPUS is pretrained on a diverse set of fluid dynamics PDEs and evaluated across 6 challenging unseen downstream PDEs spanning various physical systems. Experimental results demonstrate that SPUS using residual U-Net based architecture achieves state-of-the-art generalization on these downstream tasks while requiring significantly fewer parameters and minimal fine-tuning data, highlighting its potential as a highly parameter-efficient FM for solving diverse PDE systems.
title SPUS: A Lightweight and Parameter-Efficient Foundation Model for PDEs
topic Computer Vision and Pattern Recognition
Artificial Intelligence
Machine Learning
Computational Physics
url https://arxiv.org/abs/2510.01370