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arXiv · 2506.15687

S$^2$GPT-PINNs: Sparse and Small models for PDEs

Yajie Ji·Yanlai Chen·Shawn Koohy
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Abstract

We propose S$^2$GPT-PINN, a sparse and small model for solving parametric partial differential equations (PDEs). Similar to Small Language Models (SLMs), S$^2$GPT-PINN is tailored to domain-specific (families of) PDEs and characterized by its compact architecture and minimal computational power. Leveraging a small amount of extremely high quality data via a mathematically rigorous greedy algorithm that is enabled by the large full-order models, S$^2$GPT-PINN relies on orders of magnitude less parameters than PINNs to achieve extremely high efficiency via two levels of customizations. The first is knowledge distillation via task-specific activation functions that are transferred from Pre-Trained PINNs. The second is a judicious down-sampling when calculating the physics-informed loss of the network compressing the number of data sites by orders of magnitude to the size of the small model.

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Yajie Ji, Yanlai Chen, Shawn Koohy. 2025-05-25. S$^2$GPT-PINNs: Sparse and Small models for PDEs. https://arxiv.org/abs/2506.15687

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