Papers › UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal Adaptation

UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal Adaptation

11 Mar 2024arXiv:2403.07187archive 2025-07-28

Junhong Shen, Tanya Marwah, Ameet Talwalkar

We present Unified PDE Solvers (UPS), a data- and compute-efficient approach to developing unified neural operators for diverse families of spatiotemporal PDEs from various domains, dimensions, and resolutions. UPS embeds different PDEs into a shared representation space and processes them using a FNO-transformer architecture. Rather than training the network from scratch, which is data-demanding and computationally expensive, we warm-start the transformer from pretrained LLMs and perform explicit alignment to reduce the modality gap while improving data and compute efficiency. The cross-modal UPS achieves state-of-the-art results on a wide range of 1D and 2D PDE families from PDEBench, outperforming existing unified models using 4 times less data and 26 times less compute. Meanwhile, it is capable of few-shot transfer to unseen PDE families and coefficients.

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