# MindSpore Flow ## MindSpore Flow Introduction Fluid simulation refers to solving the governing equations of fluid dynamics under given boundary conditions through numerical computation, enabling analysis, prediction, and control of flow behaviors. It has been widely applied in engineering design across industries such as aerospace, shipbuilding, and energy/power. Traditional numerical methods for fluid simulation (e.g., finite volume and finite difference methods), mainly implemented through commercial software, involve multiple complex steps including physical modeling, mesh generation, numerical discretization, and iterative solving, resulting in lengthy computational cycles. AI demonstrates powerful learning capabilities and natural parallel inference capabilities, which can effectively enhance the efficiency of fluid simulations. MindSpore Flow, developed based on [MindSpore](https://www.mindspore.cn/), is a fluid simulation suite supporting AI-enabled flow field simulation, aerodynamic shape design, and flow control for industries including aerospace, shipbuilding, and energy/power. It aims to provide industrial researchers, engineers, academic faculty, and students with an efficient and user-friendly AI-powered computational fluid dynamics (CFD) simulation software. ## Latest News - 🔥`2025.12.30` MindScience 1.0.0 released. MindSpore Flow applications' details: [MindSpore Flow](https://atomgit.com/mindspore-lab/mindscience/blob/master/%20RELEASE.md). The applications under the old framework will be gradually migrated to the new framework. - 🔥`2025.03.30` MindFlow 0.3.0 released. - 🔥`2024.11.04` The 2024 AI for Science Forum, hosted by Peking University’s School of Computer Science and Beijing AI for Science Institute, featured a keynote by Professor Dong Bin (Boya Distinguished Professor at PKU, Deputy Director of the International Machine Learning Research Center). He announced PDEformer-2, an end-to-end solution prediction model based on MindSpore and MindFlow, capable of directly processing arbitrary PDE forms (both time-dependent and time-independent). Pre-trained on a ~40TB dataset, PDEformer-2 can infer solutions for 2D equations with varying boundary conditions, domains, and variables, rapidly predicting solutions at arbitrary spatiotemporal points. Additionally, as a differentiable surrogate model for forward problem solution operators, PDEformer-2 supports solving inverse problems, including full-wave inversion to recover wave velocity fields from noisy spatiotemporal scatter observations. This lays a foundation for modeling diverse physical phenomena and engineering applications in fluid dynamics, electromagnetics, and beyond. [Related News](https://www.mindspore.cn/news/newschildren?id=3481&type=news) - 🔥`2024.10.13` The 3rd General Assembly of the Intelligent Fluid Mechanics Industry Consortium was successfully held in Xi’an, Shaanxi, with over 200 attendees from academia and industry. An expert presented *AI Fluid Simulation and MindSpore Practices*, highlighting MindSpore’s capabilities in whole process of AI model development and MindSpore Flow’s advancements. He also showcased collaborative innovations with consortium partners, demonstrating AI+fluid mechanics applications in national priority scenarios like large aircraft development and aerodynamic design. [Related News](https://www.mindspore.cn/news/newschildren?id=3424&type=news) - 🔥`2024.09.23` The **"PHengLEI"** Aerodynamic Shape Design Platform was launched at the "AI Empowers Aerospace Innovation" Postdoctoral Forum in Mianyang, Sichuan. Developed by the China Aerodynamics Research & Development Center using MindSpore and MindSpore Flow, this generative AI platform assists designers in conceptual aerodynamic shape design. "Fenglei" enables end-to-end shape design that meets performance metrics, supports multi-scenario/multi-type design, and ensures solution diversity. Academician Tang Zhigong introduced its technical framework and applications, stating: *"AI offers a new paradigm for aerodynamics, injecting vitality into aerospace innovation. Generative aerodynamic design accelerates conceptual design and drives intelligent transformation of aero-design methodologies."* [Related News](https://www.mindspore.cn/news/newschildren?id=3405&type=news) - 🔥`2024.07.04` At the 2024 World Artificial Intelligence Conference (WAIC) in Shanghai themed *"Governing AI for good and for all"*, China Southern Power Grid’s **"Yudian"** Intelligent Simulation Model, built on MindSpore, won the prestigious SAIL (Superior AI Leader) Award. Zheng Waisheng, General Manager of CSG’s Strategic Planning Department, explained: *"Yudian precisely delineates safety boundaries of new-type power systems and optimizes generation schedules. It dynamically adjusts grid operations to address renewable energy volatility, maximizing utilization rates while ensuring grid stability."* [Related News](https://business.cctv.com/2024/07/04/ARTICo0MOGKfEyWdRf3QTyGo240704.shtml) - 🔥`2024.03.22` MindSpore Artificial Intelligence Framework Summit 2024 was held in Beijing National Convention Center. Professor Dong Bin, affiliated with both the Beijing International Center for Mathematical Research and the Center for Machine Learning Research at Peking University, revealed that the team has developed a foundation model in the realm of AI-driven PDEs, named PDEformer-1. Leveraging the MindSpore and MindFlow suites, this model is uniquely capable of directly ingesting any PDE format as input. Through extensive training on a comprehensive dataset encompassing 3 million 1D PDE samples, it has demonstrated impressive speed and precision in resolving a broad spectrum of 1D PDE forward problems. - 🔥`2024.03.22` MindSpore Artificial Intelligence Framework Summit 2024 was held in Beijing National Convention Center. Tang Zhigong, academician of Chinese Academy of Sciences and chairman of the Chinese Aerodynamic Society, introduced that the team created the generative aerodynamic design model platform based on MindSpore and MindFlow. Platform is oriented to a variety of application scenarios and breaks the traditional design paradigm. It shortens the design periods from the month level to the minute level, and meets the conceptual design requirements. [News](https://tech.cnr.cn/techph/20240323/t20240323_526636454.shtml). - 🔥`2024.03.20` MindFlow 0.2.0 is released. - 🔥`2023.11.07`The China (Xi'an) Artificial Intelligence Summit Forum was held at the High-tech International Conference Center in Yanta District, Xi'an, and the first large-scale fluid dynamics model for aircraft, "Qinling·AoXiang", jointly developed by Northwestern Polytechnical University and Huawei, was officially released. The model is an intelligent model for aircraft fluid simulation jointly developed by the International Joint Institute of Fluid Mechanics and Intelligence of Northwestern Polytechnical University and Huawei AI4Sci Lab on the basis of the domestic open-source fluid computing software Fenglei, relying on the surging computing power of Ascend AI and the MindSpore AI framework, [page](https://mp.weixin.qq.com/s/Rhpiyf3VJYm_lMBWTRDtGA). - 🔥`2023.08.02` MindFlow 0.1.0 is released, [Page](https://mindspore.cn/mindflow/docs/zh-CN/r0.1/index.html). - 🔥`2023.07.06` The 2023 World Artificial Intelligence Conference with the theme of "Connect the World Intelligently. Generate the Future" was successfully held at the Shanghai World Expo Center. The 3D Supercritical airfoil fluid simulation AI model "Dongfang Yifeng" from Comac Shanghai Aircraft Design and Research Institute won the SAIL Award, the highest award of the World Artificial Intelligence Conference. This model is a large intelligent AI model for wing complex flow simulation scenarios jointly developed by Comac Co., Ltd. Shanghai Aircraft Design and Research Institute and Huawei based on the domestic Shengteng AI basic software and hardware platform and MindSpore AI framework, [Page](https://www.thepaper.cn/newsDetail_forward_23769936). - 🔥`2023.05.21` The second plenary meeting of the intelligent fluid mechanics industrial consortium was successfully held in Hangzhou West Lake University, and Shengsi MindSpore co organized the meeting. Three academicians of the CAS Member, representatives of the industrial consortium and experts from the academic and industrial circless who care about the consortium attended the meeting. The first fluid mechanics model for aircraft - "Qinling · AoXiang" model is pre released. This model is an intelligent model for aircraft fluid simulation jointly developed by the International Joint Institute of Fluid Mechanics Intelligence of Northwestern Polytechnical University and Huawei based on the domestic Shengteng AI basic software and hardware platform and MindSpore AI framework.[Page](http://science.china.com.cn/2023-05/23/content_42378458.htm). - 🔥`2023.02.05` [MindFlow 0.1.0-alpha](https://mindspore.cn/mindflow/docs/zh-CN/r0.1.0-alpha/index.html) is released. - 🔥`2023.01.17` [MindFlow-CFD](https://zhuanlan.zhihu.com/p/599592997), an End-to-End Differentiable Solver based on MindSpore, [see more](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/mindflow/cfd). - 🔥`2022.09.02` Academician Guanghui Wu, Chief Scientist of COMAC, released the first industrial flow simulation model "DongFang.YuFeng" at WAIC2022 World Artificial Intelligence Conference. AI flow simulation assisted the aerodynamic simulation of domestic large aircraft. [Page](http://www.news.cn/fortune/2022-09/06/c_1128978806.htm). ## Publications [2024] Li X, Deng Z, Feng R, et al. Deep learning-based reduced order model for three-dimensional unsteady flow using mesh transformation and stitching[J]. Computers & Fluids. [[Paper]](https://arxiv.org/pdf/2307.07323) [2024] Wang Q, Ren P, Zhou H, et al. P $^ 2$ C $^ 2$ Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics[J]. arXiv preprint. [[Paper]](https://arxiv.org/pdf/2411.00040) [2024] Zeng B, Wang Q, Yan M, et al. PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems[J]. arXiv preprint. [[Paper]](https://arxiv.org/pdf/2410.01337) [2024] Ye Z, Huang X, Chen L, et al. Pdeformer-1: A foundation model for one-dimensional partial differential equations[J]. arXiv preprint. [[Paper]](https://arxiv.org/pdf/2407.06664) [2024] Li Z, Wang Y, Liu H, et al. Solving the boltzmann equation with a neural sparse representation[J]. SIAM Journal on Scientific Computing. [[Paper]](https://arxiv.org/pdf/2302.09233) [2024] Ye Z, Huang X, Chen L, et al. Pdeformer: Towards a foundation model for one-dimensional partial differential equations[J]. arXiv preprint. [[Paper](https://arxiv.org/abs/2402.12652)] [2024] Ye Z, Huang X, Liu H, et al. Meta-Auto-Decoder: A Meta-Learning Based Reduced Order Model for Solving Parametric Partial Differential Equations[J]. Communications on Applied Mathematics and Computation. [[Paper]](https://link.springer.com/article/10.1007/s42967-023-00293-7) [2024] Li Z, Wang Y, Liu H, et al. Solving Boltzmann equation with neural sparse representation[J]. SIAM Journal on Scientific Computing. [[Paper]](https://epubs.siam.org/doi/abs/10.1137/23M1558227?journalCode=sjoce3) [[Code]](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/boltzmann) [2023] Deng Z, Wang J, Liu H, et al. Prediction of transactional flow over supercritical airfoils using geometric-encoding and deep-learning strategies[J]. Physics of Fluids. [[Paper]](https://pubs.aip.org/aip/pof/article-abstract/35/7/075146/2903765/Prediction-of-transonic-flow-over-supercritical?redirectedFrom=fulltext) [[Code]](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/airfoil/2D_steady) [2023] Rao C, Ren P, Wang Q, et al. Encoding physics to learn reaction–diffusion processes[J]. Nature Machine Intelligence. [[Paper]](https://arxiv.org/abs/2106.04781) [[Code]](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_mechanism_fusion/percnn) [2023] Deng Z, Liu H, Shi B, et al. Temporal predictions of periodic flows using a mesh transformation and deep learning-based strategy[J]. Aerospace Science and Technology. [[Paper]](https://www.sciencedirect.com/science/article/pii/S1270963822007556) [2022] Huang X, Liu H, Shi B, et al. A Universal PINNs Method for Solving Partial Differential Equations with a Point Source[C]. IJCAI. [[Paper]](https://gitee.com/link?target=https%3A%2F%2Fwww.ijcai.org%2Fproceedings%2F2022%2F0533.pdf) [[Code]](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/poisson/point_source) ## Applications ### Data Driven | Case | Dataset | Network | GPU | NPU | | :---------------------------------------------------------------------------------------------------------------------------------------------: | :----------------------------------------------------------------------------------------------------------------------------------------: | :-------------: | :-: | :-: | |[GINO Large-scale 3D PDEs Solver](?) | [3D NS Equations Dataset](?) | FNO & GNO | - | ✔️ | | [DongFang.YuFeng](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/airfoil/2D_steady) | [2D Airfoil Flow Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/airfoil/2D_steady/) | ViT | ✔️ | ✔️ | | [Solve Burgers Equation by FNO](https://atomgit.com/mindspore-lab/mindscience/tree/master/MindFlow/applications/data_driven/burgers/fno1d) | [1D Burgers Equation Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/burgers/) | FNO1D | ✔️ | ✔️ | | [Solve Burgers Equation by KNO](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/burgers/kno1d) | [1D Burgers Equation Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/burgers/) | KNO1D | ✔️ | ✔️ | | [Solve Burgers Equation by SNO](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/burgers/sno1d) | [1D Burgers Equation Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/burgers/) | SNO1D | ✔️ | ✔️ | | [Solve Navier-Stokes Equation by FNO](https://atomgit.com/mindspore-lab/mindscience/tree/master/MindFlow/applications/data_driven/navier_stokes/fno2d) | [2D Navier-Stokes Equation Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/navier_stokes/) | FNO2D | ✔️ | ✔️ | | [Solve Navier-Stokes Equation by SNO](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/navier_stokes/sno2d) | [2D Navier-Stokes Equation Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/navier_stokes/) | SNO2D | ✔️ | ✔️ | | [Solve Navier-Stokes Equation by KNO](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/navier_stokes/kno2d) | [2D Navier-Stokes Equation Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/navier_stokes/) | KNO2D | ✔️ | ✔️ | | [Solve Navier-Stokes Equation by FNO3D](https://atomgit.com/mindspore-lab/mindscience/tree/master/MindFlow/applications/data_driven/navier_stokes/fno3d) | [3D Navier-Stokes Equation Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/navier_stokes_3d/) | FNO3D | ✔️ | ✔️ | | [Solve Navier-Stokes Equation by SNO3D](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/navier_stokes/sno3d) | [3D Navier-Stokes Equation Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/navier_stokes_3d/) | SNO3D | ✔️ | ✔️ | | [Solve 2D Riemann Problem by CAE-LSTM](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/cae_lstm) | [2D Riemann Problem Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/cae-lstm/riemann/) | CAE-LSTM | ✔️ | ✔️ | | [Solve Shu-Osher Problem by CAE-LSTM](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/cae_lstm) | [1D Shu-Osher Problem Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/cae-lstm/shu_osher/) | CAE-LSTM | ✔️ | ✔️ | | [Solve 1D Sod Shock Tube Problem by CAE-LSTM](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/cae_lstm) | [1D Sod Problem Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/cae-lstm/sod/) | CAE-LSTM | ✔️ | ✔️ | | [Solve KH Problem by CAE-LSTM](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/cae_lstm/) | [2D K-H Problem Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/cae-lstm/kh/) | CAE-LSTM | ✔️ | ✔️ | | [Solve 2D Airfoil Buffet by eHDNN](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/transonic_buffet_ehdnn) | [2D Airfoil Buffet Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/airfoil/2D_unsteady/) | eHDNN | ✔️ | ✔️ | | [Predict Unsteady Flow Fields with Move Boundary by eHDNN](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/move_boundary_hdnn) | [Move Boundary eHdnn Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/move_boundary_hdnn) | eHDNN | ✔️ | ✔️ | | [Solve 3D Unsteady Sphere Flow by ResUnet3D](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/flow_around_sphere) | [3D Unsteady Flow Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/3d_unsteady_flow/) | ResUnet3D | ✔️ | ✔️ | | [Solve 2D Cylinder Flow by CAE-Transformer](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/cae_transformer) | [Low Reynolds Cylinder Flow Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_driven/cae-transformer/) | CAE-Transformer | ✔️ | ✔️ | |[Predict Multi-timestep Complicated Transonic Airfoil by FNO2D and UNET2D](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_driven/airfoil/2D_unsteady) | [2D Transonic Airfoil Dataset](https://download-mindspore.osinfra.cn/mindscience/mindflow/dataset/applications/data_driven/airfoil/2D_unsteady/) | FNO2D/UNET2D | ✔️ | ✔️ | |[Predict Fluid-structure Interaction System by HDNN](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/fluid_structure_interaction) | [Fluid-structure Interaction System Dataset](https://download-mindspore.osinfra.cn/mindscience/mindflow/dataset/applications/data_driven/fluid_structure_interaction/) | HDNN | ✔️ | ✔️ | |[Prediction of spatiotemporal field of pulsation velocity in cylindrical wake by Cascade Net](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/cascade_net) | [CascadeNet Cylinder Wake Pulsating Dataset](https://download-mindspore.osinfra.cn/mindscience/mindflow/dataset/applications/research/Cascade_Net/) | CascadeNet | ✔️ | ✔️ | |[MultiScaleGNN for Solving Pressure Poisson Equation](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/multiscale_gnn) | [MultiScaleGNN Pressure Poisson Equation](https://download-mindspore.osinfra.cn/mindscience/mindflow/dataset/applications/research/MultiScaleGNN/) | MultiScaleGNN | ✔️ | ✔️ | |[Turbine Stage Flow Field Prediction and Uncertainty Optimization Design Based on Neural Operator Networks](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/turbine_uq) | [Turbine Cascade Meridional Flow Field Dataset](https://gitee.com/link?target=https%3A%2F%2Fdownload-mindspore.osinfra.cn%2Fmindscience%2Fmindflow%2Fdataset%2Fapplications%2Fresearch%2Fturbine_uq%2F) | UNet/FNO | ✔️ | ✔️ | ### Data-Mechanism Fusion | Case | Dataset | Network | GPU | NPU | | :--------------------------------------------------------------------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------------------------------------: | :-----: | :-: | :-: | |[P2C2Net](https://atomgit.com/mindspore-lab/mindscience/tree/master/MindFlow/applications/data_mechanism_fusion/p2c2net) | [2D Self-generated PDE Dataset](https://atomgit.com/mindspore-lab/mindscience/blob/master/MindFlow/applications/data_mechanism_fusion/p2c2net/src/data_gen.py) | P2C2Net | - | ✔️ | | [Solve Convection-Diffusion Equation by PDE-NET](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_mechanism_fusion/pde_net) | - | PDE-Net | ✔️ | ✔️ | | [Solve 2D Burgers Equation by PeRCNN](https://atomgit.com/mindspore-lab/mindscience/legacy-master/MindFlow/applications/data_mechanism_fusion/percnn/burgers_2d) | [PeRCNN Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_mechanism_fusion/PeRCNN/) | PeRCNN | ✔️ | ✔️ | | [Solve 3D Reaction-Diffusion Equation by PeRCNN](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_mechanism_fusion/percnn/gsrd_3d) | [PeRCNN Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/data_mechanism_fusion/PeRCNN/) | PeRCNN | ✔️ | ✔️ | | [AI Turb Model](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_mechanism_fusion/ai_turbulence_modeling) | - | MLP | ✔️ | ✔️ | | [Physics-encoded Message Passing Graph Network PhyMPGN solving spatiotemporal PDE systems](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/data_mechanism_fusion/phympgn) | [PhyMPGN dataset](https://download-mindspore.osinfra.cn/mindscience/mindflow/dataset/applications/data_mechanism_fusion/PhyMPGN/) | PhyMPGN | | ✔️ | | [Physical Field Prediction Model Driven by Data and Physics Hybridization](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/heat_conduction) | [Allen-Cahn dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/periodic_hill_2d/) | UNet2D | ✔️ | ✔️ | | [Fusion of Physical Mechanism for Predicting Complex Flow Temperature Fields](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/superposition) | _ | SDNO | ✔️ | ✔️ | ### Physics Driven | Case | Dataset | Network | GPU | NPU | | :----------------------------------------------------------------------------------------------------------------------------------------------------: | :--------------------------------------------------------------------------------------------------------------------------------------------: | :-----: | :-: | :-: | | [Solve Burgers Equation by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/burgers) | [Burgers Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/physics_driven/burgers_pinns/) | PINNs | ✔️ | ✔️ | | [Solve 2D Cylinder Flow by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/navier_stokes/cylinder_flow_forward) | [2D Cylinder Fow Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/physics_driven/flow_past_cylinder/) | PINNs | ✔️ | ✔️ | | [Solve 2D Darcy Problem by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/darcy) | - | PINNs | ✔️ | ✔️ | | [Solve Poisson Equation by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/poisson/continuous) | - | PINNs | ✔️ | ✔️ | | [Solve Boltzmann Equation by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/boltzmann) | - | PINNs | ✔️ | ✔️ | | [Solve 2D Taylor-Green Votex by PINNs](https://atomgit.com/mindspore-lab/mindscience/legacy-master/MindFlow/applications/physics_driven/navier_stokes/taylor_green) | - | PINNs | ✔️ | ✔️ | | [Solve Inverse Navier-Stoken Problem by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/navier_stokes/cylinder_flow_inverse) | [Navier-Stoken Inverse Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/physics_driven/inverse_navier_stokes/) | PINNs | ✔️ | ✔️ | | [Solve 2D Poisson Equation with Point Source by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/poisson/point_source) | - | PINNs | ✔️ | ✔️ | | [Solve Kovasznay Flow by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/navier_stokes/kovasznay) | - | PINNs | ✔️ | ✔️ | | [Solve Periodic Hill Flow by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/physics_driven/navier_stokes/periodic_hill) | [Periodic Hill Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/periodic_hill_2d/) | PINNs | ✔️ | ✔️ | | [Solve Allen-Cahn Equation by PINNs](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/allen_cahn) | [Allen-Cahn Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/research/allen_cahn/) | PINNs | ✔️ | ✔️ | | [CMA-ES&Multi-objective Gradient Descent Algorithm Accelerates PINNs Convergence](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/cma_es_mgda) | [Periodic Hill Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/periodic_hill_2d/) | PINNs | ✔️ | ✔️ | |[META-PINNs Algorithm](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/meta_pinns) | - | PINNs | ✔️ | ✔️ | |[MOE-PINNs Algorithm](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/moe_pinns) | - | PINNs | ✔️ | ✔️ | |[R-DLGA Algorithm](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/r_dlga) | - | PINNs | ✔️ | ✔️ | |[NSFNets: Physics-informed neural networks for the incompressible Navier-Stokes equations](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/research/nsf_nets) | - | NSFNets | ✔️ | ✔️ | ### CFD | Case | Numerical Scheme | GPU | NPU | | :-----------------------------------------------------------------------------------------------------------: | :-----: | :-: | :-- | |[2D/3D Acoustic Wave Equation CBS Solver](https://atomgit.com/mindspore-lab/mindscience/tree/master/MindFlow/applications/cfd/acoustic) | CBS | [2D/3D Acoustic Wave Dataset](https://download.mindspore.cn/mindscience/mindflow/dataset/applications/cfd/acoustic/) | - | ✔️ | | [Sod Shock Tube](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/cfd/sod) | Rusanov | ✔️ | - | | [Lax Shock Tube](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/cfd/lax) | Rusanov | ✔️ | - | | [2D Riemann Problem](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/cfd/riemann2d) | - | ✔️ | - | | [Couette Flow](https://atomgit.com/mindspore-lab/mindscience/tree/legacy-master/MindFlow/applications/cfd/couette) | - | ✔️ | - | ## Community ### Join MindScience SIG

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RenMin University of China SunHao

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[Join](https://mp.weixin.qq.com/s/e00lvKx30TsqjRhYa8nlhQ) MindSpore [MindScience SIG](https://www.mindspore.cn/sig/MindSpore%20Science) to help AI fluid simulation development. MindSpore AI for Science, [Learning and Learning to solve PDEs](https://www.bilibili.com/video/BV1ur4y1H7vB?p=4) topic report by Dong Bin, Peking University. We will continue to release [open source internship tasks](https://atomgit.com/mindspore-lab/mindscience/issues/312), build MindSpore Flow ecology with you, and promote the development of computational fluid dynamics with experts, professors and students in the field. Welcome to actively claim the task. ### Core Contributor Thanks goes to these wonderful people 🧑‍🤝‍🧑: yufan, wangzidong, liuhongsheng, zhouhongye, zhangyi, dengzhiwen, liulei, guoboqiang, chengzeruizhi, libokai, yangge, longzichao, qiuyisheng, haojiwei, leiyixiang, huangxiang, huxin,xingzhongfan, mengqinghe, lizhengyi, lixin, liuziyang, dujiaoxi, xiaoruoye, liangjiaming, zoujingyuan, wanghaining, juliagurieva, guoqicheng, chenruilin, chenchao, wangqineng, wubingyang, zhaoyifan ### Community Partners

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