第40卷第2期2023年3月新疆大学学报（自然科学版）（中英文）JournalofXinjiangUniversity(NaturalScienceEditioninChineseandEnglish)Vol.40,No.2Mar.,2023Multi-ScaleNeuralNetworksBasedonRunge-KuttaMethodforSolvingUnsteadyPartialDifferentialEquations∗CHENZebin,FENGXinlong†(SchoolofMathematicsandSystemSciences,XinjiangUniversity,UrumqiXinjiang830017,China)Abstract:Thispaperproposesthemulti-scaleneuralnetworksmethodbasedonRunge-Kuttatosolveunsteadypartialdif-ferentialequations.Themethodusesq-orderRunge-Kuttatoconstructthetimeiterationescheme,andfurtherestablishesthetotallossfunctionofmultipletimesteps,whichistorealizetheparametersharingofneuralnetworkswithmultipletimesteps,andtopredictthefunctionvalueatanymomentinthetimedomain.Besides,them-scalingfactorisadoptedtospeeduptheconvergenceofthelossfunctionandimprovetheaccuracyofthenumericalsolution.Finally,severalnumericalexperimentsarepresentedtodemonstratetheeffectivenessoftheproposedmethod.Keywords:unsteadypartialdifferentialequations;q-orderRunge-Kuttamethod;multi-scaleneuralnetworks;m-scalingfactor;highaccuracyDOI：10.13568/j.cnki.651094.651316.2022.06.25.0001CLCnumber：O175DocumentCode：AArticleID：2096-7675(2023)02-0142-08引文格式：陈泽斌,冯新龙.Runge-Kutta型多尺度神经网络求解非定常偏微分方程[J].新疆大学学报(自然科学版)(中英文),2023,40(2):142-149.英文引文格式：CHENZebin,FENGXinlong.Multi-scaleneuralnetworksbasedonRunge-Kuttamethodforsolvingunsteadypartialdifferentialequations[J].JournalofXinjiangUniversity(NaturalScienceEditioninChineseandEnglish),2023,40(2):142-149.Runge-Kutta型多尺度神经网络求解非定常偏微分方程陈泽斌,冯新龙(新疆大学数学与系统科学学院，新疆乌鲁木齐830017)摘要：提出了基于Runge-Kutta的多尺度神经网络方法求解非定常偏微分方程.利用q阶Runge-Kutta构造时间迭代格式,通过建立多时间步的总损失函数,实现多时间步的神经网络参数共享,并预测时域内任意时刻的函数值.同时采用m-缩放因子加快损失函数收敛,提高数值解精度.最后,给出了若干数值实验验证所提方法的有效性．关键词：非定常偏微分方程;q阶Runge-Kutta法;多尺度神经网络;m-缩放因子;...
