S$^2$GPT-PINNs: Sparse and Small models for PDEs
This work addresses computational efficiency for domain-specific PDEs, but it appears incremental as it builds on existing PINN methods with customizations.
The authors tackled solving parametric partial differential equations (PDEs) by proposing S$^2$GPT-PINN, a sparse and small model that uses orders of magnitude fewer parameters than PINNs to achieve high efficiency through customizations like knowledge distillation and down-sampling.
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.