{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/compositional-generative-multiphysics-and","title":"M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation","arxiv_id":"2412.04134","date":"2024-12-05","proceeding":null,"authors":["Tao Zhang","Zhenhai Liu","Feipeng Qi","Yongjun Jiao","Tailin Wu"],"abstract":"Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling-where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at https://github.com/AI4Science-WestlakeU/M2PDE.","url_abs":"https://arxiv.org/abs/2412.04134v3","url_pdf":"https://arxiv.org/pdf/2412.04134v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"compositional-generative-multiphysics-and","repo_url":"https://github.com/ai4science-westlakeu/m2pde","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"compositional-generative-multiphysics-and","repo_url":"https://github.com/AI4Science-WestlakeU/MultiSimDiff","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2412.04134","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}