Physics-Informed Multimodal Foundation Model for PDEs

This paper introduces PI-MFM, a novel framework that integrates physics knowledge directly into multimodal foundation models for solving partial differential equations (PDEs). The key innovation is the use of symbolic PDE representations and automatic assembly of PDE residual losses, enabling data-efficient and transferable PDE solvers. The approach is particularly effective in scenarios with limited labeled data or noisy conditions, demonstrating significant improvements over purely data-driven methods. The zero-shot fine-tuning capability is a notable achievement, allowing for rapid adaptation to unseen PDE families.