HT-PeRCNN：基于Hessian矩陣跡權(quán)重的物理編碼遞歸卷積神經(jīng)網(wǎng)絡(luò)

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中圖分類號(hào)：TP391.4 文獻(xiàn)標(biāo)識(shí)碼：A 文章編號(hào)：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)廣泛應(yīng)用于流體力學(xué)、熱力學(xué)和氣象模擬等諸多科學(xué)和工程領(lǐng)域[1-3]。（剩余19641字）