{"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/combining-differentiable-pde-solvers-and","title":"Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction","arxiv_id":"2007.04439","date":"2020-07-08","proceeding":"ICML 2020 1","authors":["Filipe de Avila Belbute-Peres","Thomas D. Economon","J. Zico Kolter"],"abstract":"Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the PDE solutions, yet the simulation results predicted from these approaches typically do not generalize well to truly novel scenarios. In this work, we develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. By combining an actual CFD simulator (run on a much coarser resolution representation of the problem) with the graph network, we show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions, while also substantially outperforming the coarse CFD simulation alone.","url_abs":"https://arxiv.org/abs/2007.04439v3","url_pdf":"https://arxiv.org/pdf/2007.04439v3.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":"combining-differentiable-pde-solvers-and","repo_url":"https://github.com/locuslab/cfd-gcn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"combining-differentiable-pde-solvers-and","repo_url":"https://github.com/PaddlePaddle/PaddleScience/tree/develop/jointContribution/CFDGCN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"paddle","reach":null}],"tasks":[{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2007.04439","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}