[{"data":1,"prerenderedAt":740},["ShallowReactive",2],{"content-query-n5GBpz1VgQ":3},{"_path":4,"_dir":5,"_draft":6,"_partial":6,"_locale":7,"title":8,"description":9,"date":10,"cover":11,"type":12,"category":13,"body":14,"_type":734,"_id":735,"_source":736,"_file":737,"_stem":738,"_extension":739},"/technology-blogs/zh/793","zh",false,"","技术干货｜MindSpore Science科学计算行业套件——MindSpore Elec电磁仿真套件","面向电子信息行业的MindSpore Elec套件","2021-11-18","https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/bb5ea1b2172c4e889e749840b9582285.png","technology-blogs","开发者分享",{"type":15,"children":16,"toc":718},"root",[17,25,34,39,46,51,75,81,88,93,138,143,158,163,168,175,180,187,192,199,204,211,223,230,237,249,256,268,275,282,291,302,309,314,321,333,340,352,359,367,382,387,396,401,425,435,440,445,452,459,468,473,486,493,502,507,520,527,537,545,560,565,570,585,590,595,600,605,617,625,643,657,664,672,680,685,692,697,708,713],{"type":18,"tag":19,"props":20,"children":22},"element","h1",{"id":21},"技术干货mindspore-science科学计算行业套件mindspore-elec电磁仿真套件",[23],{"type":24,"value":8},"text",{"type":18,"tag":26,"props":27,"children":28},"p",{},[29],{"type":18,"tag":30,"props":31,"children":33},"img",{"alt":7,"src":32},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/ece7a888f9d140ac9b919b42f7977e97.gif",[],{"type":18,"tag":26,"props":35,"children":36},{},[37],{"type":24,"value":38},"当前多种算力正在激发跨领域的应用融合，AI已经成为研究科学计算的新范式。因此我们将MindSpore拓展到科学计算领域。通过多尺度混合计算和高阶混合微分两大关键创新，将MindSpore原有的AI计算引擎升级为AI与科学计算的统一引擎，实现融合的统一加速。在此基础上，我们面向8大科学计算行业打造MindSpore Science【1】系列套件。这些行业套件包含业界领先的数据集、基础模型、预置高精度模型和前后处理工具，加速科学行业应用开发。",{"type":18,"tag":26,"props":40,"children":41},{},[42],{"type":18,"tag":30,"props":43,"children":45},{"alt":7,"src":44},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/9e747167775e45bc9ffc22bae6cd03d3.jpg",[],{"type":18,"tag":26,"props":47,"children":48},{},[49],{"type":24,"value":50},"当前，我们推出面向电子信息行业的MindSpore Elec套件和面向生命科学行业的MindSpore Sponge套件，分别实现了电磁仿真性能提升10倍和生物制药化合物模拟效率提升50%。下面将首先介绍MindSpore Elec套件。",{"type":18,"tag":52,"props":53,"children":55},"h3",{"id":54},"_01-mindspore-elec架构图",[56,62,64,69,70],{"type":18,"tag":57,"props":58,"children":59},"strong",{},[60],{"type":24,"value":61},"01",{"type":24,"value":63}," ",{"type":18,"tag":57,"props":65,"children":66},{},[67],{"type":24,"value":68},"Min****dSpore",{"type":24,"value":63},{"type":18,"tag":57,"props":71,"children":72},{},[73],{"type":24,"value":74},"Elec架构图",{"type":18,"tag":52,"props":76,"children":78},{"id":77},"mindspore-elec电磁仿真套件主要由前后处理工具数据构建及转换结果可视化ai电磁模型",[79],{"type":24,"value":80},"MindSpore Elec电磁仿真套件主要由前后处理工具（数据构建及转换、结果可视化）、AI电磁模型",{"type":18,"tag":26,"props":82,"children":83},{},[84],{"type":18,"tag":30,"props":85,"children":87},{"alt":7,"src":86},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/c91a0197503f4c1b925be8566cd7734c.jpg",[],{"type":18,"tag":26,"props":89,"children":90},{},[91],{"type":24,"value":92},"库（物理方程驱动和标签数据驱动）以及优化策略（数据压缩、动态自适应加权等）等组成，同时支持时域和频域的电磁仿真。以下是具体模块及功能：",{"type":18,"tag":94,"props":95,"children":96},"ol",{},[97,108,118,128],{"type":18,"tag":98,"props":99,"children":100},"li",{},[101,106],{"type":18,"tag":57,"props":102,"children":103},{},[104],{"type":24,"value":105},"数据构建及转换",{"type":24,"value":107},"：支持CSG（Constructive Solid Geometry，CSG）模式的几何构建，如矩形、圆形等结构的交集、并集和差集，以及cst和stp数据（CST等商业软件支持的数据格式）的高效张量转换。未来还会支持智能网格剖分，供传统科学计算使用。",{"type":18,"tag":98,"props":109,"children":110},{},[111,116],{"type":18,"tag":57,"props":112,"children":113},{},[114],{"type":24,"value":115},"AI电磁模型库",{"type":24,"value":117},"：提供物理和数据驱动的AI电磁模型：物理驱动是指网络的训练无需额外的标签数据，只需方程和初边界条件即可；数据驱动是指训练需使用仿真或实验等产生的数据。物理驱动相比数据驱动，优势在于可避免数据生成带来的成本和网格独立性等问题，劣势在于需明确方程的具体表达形式并克服点源奇异性、多任务损失函数以及泛化性等技术挑战。",{"type":18,"tag":98,"props":119,"children":120},{},[121,126],{"type":18,"tag":57,"props":122,"children":123},{},[124],{"type":24,"value":125},"优化策略",{"type":24,"value":127},"：为提升物理和数据驱动模型的精度、减少训练的成本，提供了一系列优化措施。数据压缩可以有效地减少神经网络的存储和计算量；多尺度滤波、动态自适应加权可以提升模型的精度，克服点源奇异性等问题；小样本学习主要是为了减少训练的数据量，节省训练的成本。",{"type":18,"tag":98,"props":129,"children":130},{},[131,136],{"type":18,"tag":57,"props":132,"children":133},{},[134],{"type":24,"value":135},"结果可视化",{"type":24,"value":137},"：仿真的结果如S参数或电磁场等可保存在CSV、VTK文件中。MindSpore Insight可以显示训练过程中的损失函数变化，并以图片的形式在网页上展示结果；Paraview是第三方开源软件，具有动态展示切片、翻转等高级功能。",{"type":18,"tag":26,"props":139,"children":140},{},[141],{"type":24,"value":142},"下面将围绕物理驱动和数据驱动的AI电磁仿真展开介绍。",{"type":18,"tag":52,"props":144,"children":146},{"id":145},"_02-物理驱动的ai电磁仿真",[147,152,153],{"type":18,"tag":57,"props":148,"children":149},{},[150],{"type":24,"value":151},"02",{"type":24,"value":63},{"type":18,"tag":57,"props":154,"children":155},{},[156],{"type":24,"value":157},"物理驱动的AI电磁仿真",{"type":18,"tag":26,"props":159,"children":160},{},[161],{"type":24,"value":162},"目前具有代表性的物理驱动的AI方法是美国布朗大学George Em Karniadakis教授课题组提出的物理信息神经网络（Physics Informed Deep Learning，PINNs）【2】。PINNs方法的核心是将方程求解转化成优化问题，极大简化了方程的建模和求解过程。但PINNs方法也有其不足的地方，如无法有效处理物理场梯度趋于无穷大的场景，无法解决多个损失函数的优化问题，尤其是数量级差异较大的问题；另外，不具备求解一类方程的能力，当方程中的特征参数（如电磁方程中介电系数等）发生变化时需要重新训练，增加了求解时间，端到端性能相比经典方法优势不是很大。",{"type":18,"tag":26,"props":164,"children":165},{},[166],{"type":24,"value":167},"在MindSpore Elec中，通过高斯分布函数平滑、结合sin激活函数的多尺度残差网络结构以及自适应加权的多任务学习策略，可以有效解决奇异性、多任务损失函数优化难等问题；此外，通过将可变参数进行编码，实现神经网络的增量训练，当参数发生变化时，通过微调可以得到新方程的解。下面将以模拟2D TE波为例，介绍MindSpore Elec求解麦克斯韦方程族的具体流程，2D TE波方程如下：",{"type":18,"tag":26,"props":169,"children":170},{},[171],{"type":18,"tag":30,"props":172,"children":174},{"alt":7,"src":173},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/dc23acc8dc7c40eeb22ca84a10a04e2c.jpg",[],{"type":18,"tag":26,"props":176,"children":177},{},[178],{"type":24,"value":179},"其中，E，H分别表示电场和磁场；ϵ, μ分别是介质的绝对介电常数、绝对磁导率；J(x,t)是电磁仿真过程中的激励源，通常表现为端口脉冲的形式。这在数学意义上近似为狄拉克函数形式所表示的点源，可以表示为：",{"type":18,"tag":26,"props":181,"children":182},{},[183],{"type":18,"tag":30,"props":184,"children":186},{"alt":7,"src":185},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/1b24fd6a579c4a7696efe99f154b733f.jpg",[],{"type":18,"tag":26,"props":188,"children":189},{},[190],{"type":24,"value":191},"其中x0为激励源位置，g(t)为脉冲信号的函数表达形式。初始条件如下：",{"type":18,"tag":26,"props":193,"children":194},{},[195],{"type":18,"tag":30,"props":196,"children":198},{"alt":7,"src":197},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/4248c8e7722f41718e24388e833f6bf5.jpg",[],{"type":18,"tag":26,"props":200,"children":201},{},[202],{"type":24,"value":203},"边界条件为二阶Mur吸收边界条件：",{"type":18,"tag":26,"props":205,"children":206},{},[207],{"type":18,"tag":30,"props":208,"children":210},{"alt":7,"src":209},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/4f8896876a2e4cc1a74075ee9545736d.png",[],{"type":18,"tag":26,"props":212,"children":213},{},[214,216,221],{"type":24,"value":215},"a) ",{"type":18,"tag":57,"props":217,"children":218},{},[219],{"type":24,"value":220},"高斯分布函数平滑",{"type":24,"value":222},"：可以采用光滑的概率分布函数代替不连续的狄拉克函数，从而克服点源奇异性的问题，概率分布函数可以选择高斯分布、柯西分布等。",{"type":18,"tag":26,"props":224,"children":225},{},[226],{"type":18,"tag":30,"props":227,"children":229},{"alt":7,"src":228},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/5dae010c67f942c8a7c00a6279e8b254.jpg",[],{"type":18,"tag":26,"props":231,"children":232},{},[233],{"type":18,"tag":30,"props":234,"children":236},{"alt":7,"src":235},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/efcda0d37146427fafaa08f7ace88641.jpg",[],{"type":18,"tag":26,"props":238,"children":239},{},[240,242,247],{"type":24,"value":241},"b) ",{"type":18,"tag":57,"props":243,"children":244},{},[245],{"type":24,"value":246},"多尺度残差网络+sin激活函数",{"type":24,"value":248},"：受上交许志钦老师多尺度【3】工作的启发，采用多尺度残差网络结构以及sin激活函数（正余弦函数与电磁波信号传播形式相契合），可以有效提升网络捕捉多频信号的能力。",{"type":18,"tag":26,"props":250,"children":251},{},[252],{"type":18,"tag":30,"props":253,"children":255},{"alt":7,"src":254},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/f33a37e16c9343c3b4dbf2b2ec394683.jpg",[],{"type":18,"tag":26,"props":257,"children":258},{},[259,261,266],{"type":24,"value":260},"c) ",{"type":18,"tag":57,"props":262,"children":263},{},[264],{"type":24,"value":265},"动态自适应加权",{"type":24,"value":267},"：AI计算电磁方程时，各项损失函数表现数量级的差异，导致训练收敛难。其中源项附近的损失函数值最大，其次是非源区域方程的损失函数。",{"type":18,"tag":26,"props":269,"children":270},{},[271],{"type":18,"tag":30,"props":272,"children":274},{"alt":7,"src":273},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/b35d4587820540ab883b0a76b6e18cf7.jpg",[],{"type":18,"tag":26,"props":276,"children":277},{},[278],{"type":18,"tag":30,"props":279,"children":281},{"alt":7,"src":280},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/d98721348b1b449383b1c84972c959f4.png",[],{"type":18,"tag":26,"props":283,"children":284},{},[285,287],{"type":24,"value":286},"原始自适应加权方案【4】：",{"type":18,"tag":30,"props":288,"children":290},{"alt":7,"src":289},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/fff1e3f461a14363beda4be72382c210.png",[],{"type":18,"tag":26,"props":292,"children":293},{},[294,296,300],{"type":24,"value":295},"原始的方案没有下界，会导致精度不足甚至不收敛问题，因此我们添加了超",{"type":18,"tag":30,"props":297,"children":299},{"alt":7,"src":298},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/89e8fab64ed849118088fc1a486151e9.png",[],{"type":24,"value":301},"参数",{"type":18,"tag":26,"props":303,"children":304},{},[305],{"type":18,"tag":30,"props":306,"children":308},{"alt":7,"src":307},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/f7715f0fa74e4113a3431ee5d20e7f59.png",[],{"type":18,"tag":26,"props":310,"children":311},{},[312],{"type":24,"value":313},"通过测试我们发现改进后的方案表现最好",{"type":18,"tag":26,"props":315,"children":316},{},[317],{"type":18,"tag":30,"props":318,"children":320},{"alt":7,"src":319},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/587bb69e1efc490bb633fd2a71f33ef5.jpg",[],{"type":18,"tag":26,"props":322,"children":323},{},[324,326,331],{"type":24,"value":325},"d) ",{"type":18,"tag":57,"props":327,"children":328},{},[329],{"type":24,"value":330},"增量训练",{"type":24,"value":332},"：基于隐向量和神经网络的结合对一系列方程组进行预训练。与求解单个问题不同，预训练步骤中，神经网络的输入为采样点（X）与隐向量（Z）的融合，具体如下图所示",{"type":18,"tag":26,"props":334,"children":335},{},[336],{"type":18,"tag":30,"props":337,"children":339},{"alt":7,"src":338},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/e67878d3d04d4090ae808c81f23ed106.jpg",[],{"type":18,"tag":26,"props":341,"children":342},{},[343,345,350],{"type":24,"value":344},"e) ",{"type":18,"tag":57,"props":346,"children":347},{},[348],{"type":24,"value":349},"实验结果",{"type":24,"value":351},"：增量训练的AI方法相比原始的PINNs方法，性能提升15倍以上；与Benchmark（传统的数值方法）的相对误差在5%左右。",{"type":18,"tag":52,"props":353,"children":354},{"id":7},[355],{"type":18,"tag":30,"props":356,"children":358},{"alt":7,"src":357},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/06bea4a0aaa9425db8762ccc4fceee46.jpg",[],{"type":18,"tag":52,"props":360,"children":362},{"id":361},"_1",[363],{"type":18,"tag":30,"props":364,"children":366},{"alt":7,"src":365},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/6aee4df09cb8472e90b1c6bdf9f4f590.jpg",[],{"type":18,"tag":52,"props":368,"children":370},{"id":369},"_03-数据驱动的ai电磁仿真",[371,376,377],{"type":18,"tag":57,"props":372,"children":373},{},[374],{"type":24,"value":375},"03",{"type":24,"value":63},{"type":18,"tag":57,"props":378,"children":379},{},[380],{"type":24,"value":381},"数据驱动的AI电磁仿真",{"type":18,"tag":26,"props":383,"children":384},{},[385],{"type":24,"value":386},"MindSpore Elec提供了基于参数化和点云的数据驱动方法。参数化方案实现的是参数到仿真结果的直接映射，例如天线的宽度、角度作为网络输入，网络输出为S参数。参数化方案的优点是直接映射且网络简单。点云方案实现的是从天线/手机的采样点云到仿真结果的映射，该方案先将手机结构文件转化为点云张量数据，压缩后使用卷积神经网络提取结构特征，再通过数层全连接层映射到最终的仿真结果（S参数）。该方案的优点是适用于复杂工况的结构变化，我们重点介绍下点云的数据驱动方案。",{"type":18,"tag":26,"props":388,"children":389},{},[390,391],{"type":24,"value":215},{"type":18,"tag":57,"props":392,"children":393},{},[394],{"type":24,"value":395},"从CST文件导出几何/材料信息",{"type":18,"tag":26,"props":397,"children":398},{},[399],{"type":24,"value":400},"MindSpore Elec提供两种自动化执行脚本，用于将cst格式文件转换为Python可读取的stp文件，使用该脚本可以实现数据批量转换，实现大规模电磁仿真：",{"type":18,"tag":402,"props":403,"children":404},"ul",{},[405,415],{"type":18,"tag":98,"props":406,"children":407},{},[408,413],{"type":18,"tag":57,"props":409,"children":410},{},[411],{"type":24,"value":412},"基于CST的VBA接口自动调用导出json文件和stp文件",{"type":24,"value":414},"：打开CST软件的VBA Macros Editor，导入generate_pointcloud目录下的export_stp.bas文件，将json文件和stp文件路径更改为想要存放的位置，然后点击Run即可导出json文件和stp文件。其中，json文件中包含了模型的端口位置以及stp文件对应的材料信息。",{"type":18,"tag":98,"props":416,"children":417},{},[418,423],{"type":18,"tag":57,"props":419,"children":420},{},[421],{"type":24,"value":422},"对于CST2019或更新的版本，支持使用Python直接调用CST",{"type":24,"value":424},"：直接调用generate_pointcloud目录下的export_stp.py文件即可。",{"type":18,"tag":26,"props":426,"children":427},{},[428,430],{"type":24,"value":429},"b）",{"type":18,"tag":57,"props":431,"children":432},{},[433],{"type":24,"value":434},"点云数据生成",{"type":18,"tag":26,"props":436,"children":437},{},[438],{"type":24,"value":439},"stp文件无法直接作为神经网络的输入，需要先转换为规则的张量数据，MindSpore Elec提供将stp文件高效转化为点云张量数据的接口，generate_pointcloud目录下的generate_cloud_point.py文件提供该接口调用示例。",{"type":18,"tag":26,"props":441,"children":442},{},[443],{"type":24,"value":444},"调用时，通过配置stp_path和json_path可以指定用来生成点云的stp和json文件的路径；material_dir指定stp对应的材料信息的路径，材料信息直接在cst软件中导出；sample_nums指定x、y、z三个维度分别生成多少个点云数据；bbox_args用来指定生成点云数据的区域，即（x_min, y_min, z_min, x_max, y_max, z_max）。",{"type":18,"tag":26,"props":446,"children":447},{},[448],{"type":18,"tag":30,"props":449,"children":451},{"alt":7,"src":450},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/a36adb3dadc3478aa7576bcac113eb01.jpg",[],{"type":18,"tag":26,"props":453,"children":454},{},[455],{"type":18,"tag":30,"props":456,"children":458},{"alt":7,"src":457},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/c20386752fd340b3abd5df7b5e476400.jpg",[],{"type":18,"tag":26,"props":460,"children":461},{},[462,463],{"type":24,"value":260},{"type":18,"tag":57,"props":464,"children":465},{},[466],{"type":24,"value":467},"数据压缩",{"type":18,"tag":26,"props":469,"children":470},{},[471],{"type":24,"value":472},"如果点云分辨率设置较高，仅单条点云数据的后处理就需巨大的内存和计算量，因此MindSpore Elec提供数据压缩功能。用户可以调用data_compression目录下的脚本，压缩原始点云数据，该压缩过程分两步：",{"type":18,"tag":402,"props":474,"children":475},{},[476,481],{"type":18,"tag":98,"props":477,"children":478},{},[479],{"type":24,"value":480},"首次使用时需要调用train.py训练压缩模型，若已有压缩模型检查点可以跳过该步。",{"type":18,"tag":98,"props":482,"children":483},{},[484],{"type":24,"value":485},"模型训练结束后即可调用data_compress.py进行数据压缩。",{"type":18,"tag":26,"props":487,"children":488},{},[489],{"type":18,"tag":30,"props":490,"children":492},{"alt":7,"src":491},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/053df5cc573c43308d3ac00a9ac3e6b0.jpg",[],{"type":18,"tag":26,"props":494,"children":495},{},[496,497],{"type":24,"value":325},{"type":18,"tag":57,"props":498,"children":499},{},[500],{"type":24,"value":501},"电磁仿真计算",{"type":18,"tag":26,"props":503,"children":504},{},[505],{"type":24,"value":506},"点云数据准备完毕后即可调用MindSpore Elec full_em和S_parameter目录下的电磁仿真模型，实现全量电磁场和S参数的仿真计算，每个仿真过程均可以分为如下两步：",{"type":18,"tag":402,"props":508,"children":509},{},[510,515],{"type":18,"tag":98,"props":511,"children":512},{},[513],{"type":24,"value":514},"调用train.py训练仿真模型。",{"type":18,"tag":98,"props":516,"children":517},{},[518],{"type":24,"value":519},"模型训练结束后调用eval.py进行全量电磁场或S参数的仿真计算。",{"type":18,"tag":26,"props":521,"children":522},{},[523],{"type":18,"tag":30,"props":524,"children":526},{"alt":7,"src":525},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/e83f31746dab4508b5e8c882ac140210.jpg",[],{"type":18,"tag":26,"props":528,"children":529},{},[530,531,535],{"type":24,"value":344},{"type":18,"tag":57,"props":532,"children":533},{},[534],{"type":24,"value":349},{"type":24,"value":536},"：在手机电磁仿真场景中，仿真精度媲美传统科学计算软件，同时性能提升10倍。",{"type":18,"tag":52,"props":538,"children":540},{"id":539},"_2",[541],{"type":18,"tag":30,"props":542,"children":544},{"alt":7,"src":543},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/c99c53cc2a884cbfb1d530b6327f72b0.jpg",[],{"type":18,"tag":52,"props":546,"children":548},{"id":547},"_04-总结与展望",[549,554,555],{"type":18,"tag":57,"props":550,"children":551},{},[552],{"type":24,"value":553},"04",{"type":24,"value":63},{"type":18,"tag":57,"props":556,"children":557},{},[558],{"type":24,"value":559},"总结与展望",{"type":18,"tag":26,"props":561,"children":562},{},[563],{"type":24,"value":564},"MindSpore Elec套件已构筑基础的AI电磁仿真能力，并在手机电磁仿真等场景取得技术突破。我们也欢迎广大的科学计算爱好者和研究者加入，共同拓展和维护MindSpore Elec套件。感兴趣的同学可以参考我们在arXiv上面的论文【5，6】。",{"type":18,"tag":26,"props":566,"children":567},{},[568],{"type":24,"value":569},"参考文献：",{"type":18,"tag":26,"props":571,"children":572},{},[573,575,583],{"type":24,"value":574},"[1] ",{"type":18,"tag":576,"props":577,"children":581},"a",{"href":578,"rel":579},"https://gitee.com/mindspore/mindscience/tree/master",[580],"nofollow",[582],{"type":24,"value":578},{"type":24,"value":584},".",{"type":18,"tag":26,"props":586,"children":587},{},[588],{"type":24,"value":589},"[2] Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707, 2019.",{"type":18,"tag":26,"props":591,"children":592},{},[593],{"type":24,"value":594},"[3] Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao, and Zheng Ma. Frequency principle: Fourier analysis sheds light on deep neural networks. arXiv preprint arXiv:1901.06523, 2019.",{"type":18,"tag":26,"props":596,"children":597},{},[598],{"type":24,"value":599},"[4] Alex Kendall, Yarin Gal, and Roberto Cipolla. Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7482–7491, 2018.",{"type":18,"tag":26,"props":601,"children":602},{},[603],{"type":24,"value":604},"[5] Huang X, Liu H, Shi B, et al. Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networks[J]. arXiv preprint arXiv:2111.01394, 2021.",{"type":18,"tag":26,"props":606,"children":607},{},[608,610,616],{"type":24,"value":609},"[6] Huang X, Liu H, Shi B, et al. Meta-Auto-Decoder for Solving Parametric Partial Differential Equations[J]. ",{"type":18,"tag":576,"props":611,"children":614},{"href":612,"rel":613},"https://arxiv.org/pdf/2111.08823.pdf",[580],[615],{"type":24,"value":612},{"type":24,"value":584},{"type":18,"tag":26,"props":618,"children":619},{},[620],{"type":18,"tag":57,"props":621,"children":622},{},[623],{"type":24,"value":624},"欢迎投稿",{"type":18,"tag":26,"props":626,"children":627},{},[628],{"type":18,"tag":57,"props":629,"children":630},{},[631,633,641],{"type":24,"value":632},"欢迎大家踊跃投稿，有想投稿的同学，可以添加MindSpore官方小助手：小猫子（",{"type":18,"tag":57,"props":634,"children":635},{},[636],{"type":18,"tag":57,"props":637,"children":638},{},[639],{"type":24,"value":640},"mindspore0328",{"type":24,"value":642},"）的微信，告诉猫哥哦！",{"type":18,"tag":26,"props":644,"children":645},{},[646,651,652],{"type":18,"tag":57,"props":647,"children":648},{},[649],{"type":24,"value":650},"昇思MindSpore官方交流QQ群 :",{"type":24,"value":63},{"type":18,"tag":57,"props":653,"children":654},{},[655],{"type":24,"value":656},"486831414",{"type":18,"tag":26,"props":658,"children":659},{},[660],{"type":18,"tag":30,"props":661,"children":663},{"alt":7,"src":662},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/229b3737b48d4494932d7974382a2942.jpg",[],{"type":18,"tag":26,"props":665,"children":666},{},[667],{"type":18,"tag":57,"props":668,"children":669},{},[670],{"type":24,"value":671},"官方QQ群号 : 486831414",{"type":18,"tag":26,"props":673,"children":674},{},[675],{"type":18,"tag":57,"props":676,"children":677},{},[678],{"type":24,"value":679},"微信小助手：mindspore0328",{"type":18,"tag":26,"props":681,"children":682},{},[683],{"type":24,"value":684},"扫描下方二维码加入MindSpore项目↓",{"type":18,"tag":26,"props":686,"children":687},{},[688],{"type":18,"tag":30,"props":689,"children":691},{"alt":7,"src":690},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/11/18/fe80025f9a4c4de7bd23e8de91fd181f.jpg",[],{"type":18,"tag":26,"props":693,"children":694},{},[695],{"type":24,"value":696},"MindSpore官方资料",{"type":18,"tag":26,"props":698,"children":699},{},[700,702],{"type":24,"value":701},"GitHub : ",{"type":18,"tag":576,"props":703,"children":706},{"href":704,"rel":705},"https://github.com/mindspore-ai/mindspore",[580],[707],{"type":24,"value":704},{"type":18,"tag":26,"props":709,"children":710},{},[711],{"type":24,"value":712},"Gitee : https : //gitee.com/mindspore/mindspore",{"type":18,"tag":26,"props":714,"children":715},{},[716],{"type":24,"value":717},"官方QQ群 : 486831414",{"title":7,"searchDepth":719,"depth":719,"links":720},4,[721,724,725,727,728,729,731,732],{"id":54,"depth":722,"text":723},3,"01 Min****dSpore Elec架构图",{"id":77,"depth":722,"text":80},{"id":145,"depth":722,"text":726},"02 物理驱动的AI电磁仿真",{"id":7,"depth":722,"text":7},{"id":361,"depth":722,"text":7},{"id":369,"depth":722,"text":730},"03 数据驱动的AI电磁仿真",{"id":539,"depth":722,"text":7},{"id":547,"depth":722,"text":733},"04 总结与展望","markdown","content:technology-blogs:zh:793.md","content","technology-blogs/zh/793.md","technology-blogs/zh/793","md",1776506141356]