Physics-Informed Multimodal Foundation Model for PDEs
Published:Dec 28, 2025 19:43
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
- •PI-MFM integrates physics knowledge into multimodal foundation models for solving PDEs.
- •The framework uses symbolic PDE representations and automatic assembly of PDE residual losses.
- •It outperforms data-driven methods, especially with limited data or noise.
- •Demonstrates zero-shot fine-tuning to unseen PDE families.
Reference
“PI-MFM consistently outperforms purely data-driven counterparts, especially with sparse labeled spatiotemporal points, partially observed time domains, or few labeled function pairs.”