Title: SPUS: A Lightweight and Parameter-Efficient Foundation Model for PDEs
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: foundation models, neural pde solvers, deep neural architectures

Abstract: 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.

TL;DR: Small PDE UNet Solver (SPUS) is a parameter-efficient foundation model and as accurate as medium transformers for neural PDE solvers