Deep neural networks(DNNs)have recently shown great potential in solving partial differential equations(PDEs).The success of neural network-based surrogate models is attributed to their ability to learn a rich set of ...Deep neural networks(DNNs)have recently shown great potential in solving partial differential equations(PDEs).The success of neural network-based surrogate models is attributed to their ability to learn a rich set of solution-related features.However,learning DNNs usually involves tedious training iterations to converge and requires a very large number of training data,which hinders the application of these models to complex physical contexts.To address this problem,we propose to apply the transfer learning approach to DNN-based PDE solving tasks.In our work,we create pairs of transfer experiments on Helmholtz and Navier-Stokes equations by constructing subtasks with different source terms and Reynolds numbers.We also conduct a series of experiments to investigate the degree of generality of the features between different equations.Our results demonstrate that despite differences in underlying PDE systems,the transfer methodology can lead to a significant improvement in the accuracy of the predicted solutions and achieve a maximum performance boost of 97.3%on widely used surrogate models.展开更多
基金supported by the National Numerical Windtunnel project(NNW2019ZT5-A10)the National Key Research and Development Program of China(2018YFB0204301,2017YFB0202104).
文摘Deep neural networks(DNNs)have recently shown great potential in solving partial differential equations(PDEs).The success of neural network-based surrogate models is attributed to their ability to learn a rich set of solution-related features.However,learning DNNs usually involves tedious training iterations to converge and requires a very large number of training data,which hinders the application of these models to complex physical contexts.To address this problem,we propose to apply the transfer learning approach to DNN-based PDE solving tasks.In our work,we create pairs of transfer experiments on Helmholtz and Navier-Stokes equations by constructing subtasks with different source terms and Reynolds numbers.We also conduct a series of experiments to investigate the degree of generality of the features between different equations.Our results demonstrate that despite differences in underlying PDE systems,the transfer methodology can lead to a significant improvement in the accuracy of the predicted solutions and achieve a maximum performance boost of 97.3%on widely used surrogate models.
