标题： SPUS：一种轻量级且参数高效的偏微分方程基础模型 显示英文标题

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

摘要： 我们引入了小型PDE U-Net求解器（SPUS），这是一种紧凑且高效的基座模型（FM），被设计为一种统一的神经算子，用于解决各种偏微分方程（PDEs）。 与现有最先进的PDE FM—主要基于大型复杂Transformer架构，具有高计算和参数开销—SPUS利用了一种轻量级的残差U-Net架构，该架构在该领域作为基座模型架构尚未得到充分探索。 为了在这个极简框架中实现有效的学习，我们采用了一种简单但强大的自回归预训练策略，该策略紧密复制数值求解器的行为以学习底层物理。 SPUS在多样化的流体动力学PDE集上进行预训练，并在6个具有挑战性的未见过的下游PDE上进行评估，这些PDE跨越了各种物理系统。 实验结果表明，SPUS使用基于残差U-Net的架构在这些下游任务上实现了最先进的一般化性能，同时需要显著更少的参数和最少的微调数据，突显了其作为解决多样化PDE系统的高度参数高效FM的潜力。 显示英文摘要

摘要： 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.