SimDiffPDE: Simple Diffusion Baselines for Solving Partial Differential Equations
Keywords: Partial Differential Equations, Diffusion Model, Fluid Dynamics, Machine Learning in PDEs, Generative Models
Abstract: We showcase good capabilities of the plain diffusion model with Transformers (SimDiffPDE) for general partial differential equations (PDEs) solving from various aspects, namely simplicity in model structure, scalability in model size, flexibility in training paradigm, and universality between different PDEs. Specifically, SimDiffPDE reformulates PDE-solving problems as the image-to-image translation problem, and employs plain and non-hierarchical diffusion model with Transformer to generate the solutions conditioned on the initial states/parameters of PDEs. We further propose a multi-scale noise to explicitly guide the diffusion model in capturing information of different frequencies within the solution domain of PDEs. SimDiffPDE achieves a remarkable improvement of +51.4% on the challenging Navier-Stokes equations. In benchmark tests for solving PDEs, such as Darcy Flow, Airfoil, and Pipe for fluid dynamics, as well as Plasticity and Elasticity for solid mechanics, our SimDiffPDE-B achieves significant relative improvements of +21.1%, +11.3%, +15.2%, +25.0%, and +23.4%, respectively. Models and code shall be released upon acceptance.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 2098
Loading