Summary of Diffusionpde: Generative Pde-solving Under Partial Observation, by Jiahe Huang et al.
DiffusionPDE: Generative PDE-Solving Under Partial Observation
by Jiahe Huang, Guandao Yang, Zichen Wang, Jeong Joon Park
First submitted to arxiv on: 25 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV); Numerical Analysis (math.NA)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A novel framework for solving partial differential equations (PDEs) is introduced using generative diffusion models. The proposed approach, dubbed DiffusionPDE, simultaneously fills in missing information and solves PDEs by modeling the joint distribution of solution and coefficient spaces. This method outperforms state-of-the-art methods for both forward and inverse directions in solving a wide range of PDEs under partial observation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary DiffusionPDE is a new way to solve partial differential equations when we don’t have all the information. It’s like filling in missing pieces of a puzzle while solving the equation. This approach works better than other methods for solving equations with incomplete data, which happens often in real-world measurements. |
Keywords
» Artificial intelligence » Diffusion
