We propose S2GPT-PINN, a sparse and small model for solving parametric partial differential equations (PDEs). Similar to Small Language Models (SLMs), S2GPT-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, S2GPT-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.
@article{arxiv.2506.15687,
title = {S$^2$GPT-PINNs: Sparse and Small models for PDEs},
author = {Yajie Ji and Yanlai Chen and Shawn Koohy},
journal= {arXiv preprint arXiv:2506.15687},
year = {2025}
}