SPUS: A Lightweight and Parameter-Efficient Foundation Model for PDEs
This provides a more parameter-efficient foundation model for researchers and practitioners solving diverse PDE systems in physics and engineering, though it is incremental as it adapts an existing architecture to a new domain.
The authors tackled the problem of computational inefficiency in foundation models for solving partial differential equations (PDEs) by introducing SPUS, a lightweight residual U-Net-based model that achieved state-of-the-art generalization across 6 unseen PDEs while requiring significantly fewer parameters and minimal fine-tuning data.
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.