HT-PeRCNN：基于Hessian矩阵迹权重的物理编码递归卷积神经网络

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中图分类号：TP391.4 文献标识码：A 文章编号：2096-4706（2025）11-0025-09

HT-PeRCNN: Physics-encoded Recurrent Convolutional Neural Network Based on Hessian Trace Weight

(InformationService Center,BinnanOilProductionPlantofShengli OilfeldBranch,ChinaPetroleumand ChemicalCo.,Ltd, Binzhou 256600, China)

Abstract: In recent years, Physics-Informed Neural Networks (PINNs) have achieved significant progressas a Deep Learning-basedpproachforslvingPartialDifrentialEquations (PDEs)inariousfelds.However,PNNsstillsuffrfro problemsoflow training eficiencyand slow inference speed.To address these problems,this study proposes an improved methodofPhysics-encodedRecurrentConvolutionalNeuralNetwork(PeRCNN)basedontheHesian traceweight,named HT-PeRCNN.The methoduses the Hessiantrace as a weighted factorto optimize the weighted distributionofloss function, enhancing modelstabilityand extrapolationcapability.Experimentalresults show that HT-PeRCNN improves solutionaccuracy by 50% comparedtoPeRCNNinmultiple PDE-solvingtasks.

Keywords:PDE;PINN;PeRCNN;Hessian traceweight

0 引言

偏微分方程(PartialDifferential Equations,PDEs)广泛应用于流体力学、热力学和气象模拟等诸多科学和工程领域[1-3]。（剩余19641字）