这里有个物理信息神经网络开源项目含模型软件论文

　　物理信息神经网络（PhysicsInformedNeuralNetwork，PINN）是由布朗大学应用数学的研究团队提出的一种用物理方程作为运算限制的神经网络，用于求解偏微分方程。
　　偏微分方程是物理中常用的用于分析状态随时间改变的物理系统的公式，该神经网络也因此成为AI物理领域中最常见到的框架之一。
　　PINN架构图。
　　近两年，PINN在科学计算领域取得了巨大的成功。来自智能设计与鲁棒学习（IDRL）实验室创建了一个githubrepo，列出了关于PINN的代表性工作。大家可以star、使用！（欢迎指正和建议。）
　　为方便起见，还提供了用于将bibtex转换为markdown的脚本。
　　项目地址：https：github。comidrllabPINNpapers
　　以下为项目内容列表：软件DeepXDE：ADeepLearningLibraryforSolvingDifferentialEquations，LuLu，XuhuiMeng，ZhipingMao，GeorgeEmKarniadakis，SIAMReview，2021。NVIDIASimNet：AnAIAcceleratedMultiPhysicsSimulationFramework，OliverHennigh，SusheelaNarasimhan，MohammadAminNabian，AkshaySubramaniam，KaustubhTangsali，ZhiweiFang，MaxRietmann，WonminByeon，SanjayChoudhry，ICCS，2021。SciANN：AKeraswrapperforscientificcomputationsandphysicsinformeddeeplearningusingartificialneuralnetworks，EhsanHaghighat，RubenJuanes，arXivpreprintarXiv：2005。08803，2020。Elvetaneuralnetworkbaseddifferentialequationandvariationalproblemsolver，JackY。Araz，JuanCarlosCriado，MichaelSpannowsky，arXiv：2103。14575〔heplat，physics：hepph，physics：hepth，stat〕，2021。TensorDiffEq：ScalableMultiGPUForwardandInverseSolversforPhysicsInformedNeuralNetworks，LeviD。McClenny，MulugetaA。Haile，UlissesM。BragaNeto，arXiv：2103。16034〔physics〕，2021。PyDEns：aPythonFrameworkforSolvingDifferentialEquationswithNeuralNetworks，AlexKoryagin，er，RomanKhudorozkov，SergeyTsimfer，arXiv：1909。11544〔cs，stat〕，2019。NeuroDiffEq：APythonpackageforsolvingdifferentialequationswithneuralnetworks，FeiyuChen，DavidSondak，PavlosProtopapas，MariosMattheakis，ShuhengLiu，DevanshAgarwal，MarcoDiGiovanni，JournalofOpenSourceSoftware，2020。UniversalDifferentialEquationsforScientificMachineLearning，ChristopherRackauckas，YingboMa，JuliusMartensen，CollinWarner，KirillZubov，RohitSupekar，DominicSkinner，AliRamadhan，AlanEdelman，arXiv：2001。04385〔cs，math，qbio，stat〕，2020。NeuralPDE：AutomatingPhysicsInformedNeuralNetworks（PINNs）withErrorApproximations，KirillZubov，ZoeMcCarthy，YingboMa，FrancescoCalisto，ValerioPagliarino，SimoneAzeglio，LucaBottero，EmmanuelLujn，ValentinSulzer，AshutoshBharambe，NVinchhi，，KaushikBalakrishnan，DeveshUpadhyay，ChrisRackauckas，arXiv：2107。09443〔cs〕，2021。IDRLnet：APhysicsInformedNeuralNetworkLibrary，WeiPeng，JunZhang，WeienZhou，XiaoyuZhao，WenYao，XiaoqianChen，arXiv：2107。04320〔cs，math〕，2021。PINN模型Physicsinformedneuralnetworks：Adeeplearningframeworkforsolvingforwardandinverseproblemsinvolvingnonlinearpartialdifferentialequations，M。Raissi，P。Perdikaris，G。E。Karniadakis，JournalofComputationalPhysics，2019。ThedeepRitzmethod：adeeplearningbasednumericalalgorithmforsolvingvariationalproblems，EWeinan，BingYu，CommunicationsinMathematicsandStatistics，2018。DGM：Adeeplearningalgorithmforsolvingpartialdifferentialequations，JustinSirignano，KonstantinosSpiliopoulos，JournalofComputationalPhysics，2018。SPINN：Sparse，Physicsbased，andpartiallyInterpretableNeuralNetworksforPDEs，AmuthanA。Ramabathiran，Ramach，Prabhuran，JournalofComputationalPhysics，2021。并行PINNParallelPhysicsInformedNeuralNetworksviaDomainDecomposition，KhemrajShukla，AmeyaD。Jagtap，GeorgeEmKarniadakis，arXiv：2104。10013〔cs〕，2021。FiniteBasisPhysicsInformedNeuralNetworks（FBPINNs）：ascalabledomaindecompositionapproachforsolvingdifferentialequations，BenMoseley，AndrewMarkham，TarjeNissenMeyer，arXiv：2107。07871〔physics〕，2021。PPINN：PararealphysicsinformedneuralnetworkfortimedependentPDEs，XuhuiMeng，ZhenLi，DongkunZhang，GeorgeEmKarniadakis，ComputerMethodsinAppliedMechanicsandEngineering，2020。PINN加速SelfadaptivelossbalancedPhysicsinformedneuralnetworksfortheincompressibleNavierStokesequations，ZixueXiang，WeiPeng，XiaohuZheng，XiaoyuZhao，WenYao，arXiv：2104。06217〔physics〕，2021。ADualDimermethodfortrainingphysicsconstrainedneuralnetworkswithminimaxarchitecture，DehaoLiu，YanWang，NeuralNetworks，2021。AdversarialMultitaskLearningEnhancedPhysicsinformedNeuralNetworksforSolvingPartialDifferentialEquations，PongpisitThanasutives，MasayukiNumao，KenichiFukui，arXiv：2104。14320〔cs，math〕，2021。DPM：ANovelTrainingMethodforPhysicsInformedNeuralNetworksinExtrapolation，JungeunKim，KookjinLee，DongeunLee，SheoYonJin，NoseongPark，AAAI，2021。模型迁移和元学习Aphysicsawarelearningarchitecturewithinputtransfernetworksforpredictivemodeling，AmirBehjat，ChenZeng，RahulRai，IonMatei，DavidDoermann，SoumaChowdhury，AppliedSoftComputing，2020。Transferlearningbasedmultifidelityphysicsinformeddeepneuralnetwork，SouvikChakraborty，JournalofComputationalPhysics，2021。Transferlearningenhancedphysicsinformedneuralnetworkforphasefieldmodelingoffracture，SomdattaGoswami，CosminAnitescu，SouvikChakraborty，TimonRabczuk，TheoreticalandAppliedFractureMechanics，2020。MetalearningPINNlossfunctions，ApostolosF。Psaros，KenjiKawaguchi，GeorgeEmKarniadakis，arXiv：2107。05544〔cs〕，2021。概率PINN和不确定性量化Aphysicsaware，probabilisticmachinelearningframeworkforcoarsegraininghighdimensionalsystemsintheSmallDataregime，ConstantinGrigo，PhaedonSteliosKoutsourelakis，JournalofComputationalPhysics，2019。Adversarialuncertaintyquantificationinphysicsinformedneuralnetworks，YiboYang，ParisPerdikaris，JournalofComputationalPhysics，2019。BPINNs：BayesianphysicsinformedneuralnetworksforforwardandinversePDEproblemswithnoisydata，LiuYang，XuhuiMeng，GeorgeEmKarniadakis，JournalofComputationalPhysics，2021。PIDGAN：AGANFrameworkbasedonaPhysicsinformedDiscriminatorforUncertaintyQuantificationwithPhysics，ArkaDaw，M。Maruf，AnujKarpatne，arXiv：2106。02993〔cs，stat〕，2021。QuantifyingUncertaintyinPhysicsInformedVariationalAutoencodersforAnomalyDetection，MarcusJ。Neuer，ESTEP，2020。应用Physicsinformedneuralnetworksforhighspeedflows，ZhipingMao，AmeyaD。Jagtap，GeorgeEmKarniadakis，ComputerMethodsinAppliedMechanicsandEngineering，2020。Surrogatemodelingforfluidflowsbasedonphysicsconstraineddeeplearningwithoutsimulationdata，LuningSun，HanGao，ShaowuPan，JianXunWang，ComputerMethodsinAppliedMechanicsandEngineering，2020。Hiddenfluidmechanics：Learningvelocityandpressurefieldsfromflowvisualizations，MaziarRaissi，AlirezaYazdani，GeorgeEmKarniadakis，Science，2020。NSFnets（NavierStokesflownets）：PhysicsinformedneuralnetworksfortheincompressibleNavierStokesequations，XiaoweiJin，ShengzeCai，HuiLi，GeorgeEmKarniadakis，JournalofComputationalPhysics，2021。AHighEfficientHybridPhysicsInformedNeuralNetworksBasedonConvolutionalNeuralNetwork，ZhiweiFang，IEEETransactionsonNeuralNetworksandLearningSystems，2021。AStudyonaFeedforwardNeuralNetworktoSolvePartialDifferentialEquationsinHyperbolicTransportProblems，EduardoAbreu，JoaoB。Florindo，ICCS，2021。PINN分析EstimatesonthegeneralizationerrorofphysicsinformedneuralnetworksforapproximatingaclassofinverseproblemsforPDEs，SiddharthaMishra，RobertoMolinaro，IMAJournalofNumericalAnalysis，2021。Erroranalysisforphysicsinformedneuralnetworks（PINNs）approximatingKolmogorovPDEs，TimDeRyck，SiddharthaMishra，arXiv：2106。14473〔cs，math〕，2021。ErrorAnalysisofDeepRitzMethodsforEllipticEquations，YulingJiao，YanmingLai，YisuLuo，YangWang，YunfeiYang，arXiv：2107。14478〔cs，math〕，2021。
　　项目地址：https：github。comidrllabPINNpapers