S$^2$GPT-PINNs: Sparse and Small models for PDEs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908413125984256 |
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| author | Ji, Yajie Chen, Yanlai Koohy, Shawn |
| author_facet | Ji, Yajie Chen, Yanlai Koohy, Shawn |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | S$^2$GPT-PINNs: Sparse and Small models for PDEs Ji, Yajie Chen, Yanlai Koohy, Shawn Machine Learning 65M70, 65N99, 68U99, 68T07 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. |
| title | S$^2$GPT-PINNs: Sparse and Small models for PDEs |
| topic | Machine Learning 65M70, 65N99, 68U99, 68T07 |
| url | https://arxiv.org/abs/2506.15687 |