Research On Inverse Source Problem Based On Neural Network

The inverse source problem has been widely used in many fields,such as pollution source search,and earthquake monitoring.This paper mainly focuses on the reconstruction of the location and magnitude of the point sources from far-field data.Aiming at the inverse source problem in elastic wave for reconstructing the location and magnitude of the sources from far-field data generated under different aperture conditions,this paper constructs two neural network models: fully connected neural network model and dual-driven neural network model.Take the far-field data as the input,and take the parameters of the location and magnitude as output of the neural network,design a neural network model.The model applies Adam algorithm to update the weight and bias,and solves the problem of using far-field data to reconstruct the location and magnitude of the point sources.The fully connected neural network model is a data-driven parameters reconstruction model of the location and magnitude of the point sources.According to the far-field data and the location and magnitude parameters of the point sources,the model updates the parameters of the model by self-learning,and then reconstructs the location and magnitude parameters of the point sources.The experimental results indicate that the model can solve the inverse source problem for elastic wave,and the experiments under the conditions of noise and finite observation aperture respectively indicate that the model can effectively solve the inverse source problem of position and intensity parameters of point sources.The model structure is simple,and the location and magnitude parameters of the point sources can be better reconstructed.In order to improve the accuracy of reconstruction parameters and increase the interpretability of the network,consider improving the complexity of the network and adding the physical model to the neural network to construct a dual-driven neural network model.The model consists of two modules: physical and data.The data-driven module is a neural network with far-field data as input and location and magnitude parameters as output.The physical-driven module substitutes the location and magnitude parameters of the output by the data-driven module into its satisfied Lam é system to calculate the corresponding far-field data.By comparing the real output and labels of the two modules,the loss of the two modules is obtained.Then the loss weighted sum is used as the driving force for the evolution of the driver solver,and then the weight and bias of the neural network is updated through the Adam optimization algorithm to achieve the effect of updating the dual-driven neural network.The update of the physical-driven module depends on the input of the module,and finally the dual-driven neural network is obtained.The dual-driven neural network has the following two characteristics.First,the solver retains the original characteristics of the neural network,and the method is easy to effective and implement.Second,the introduction of the physical-driven module takes the Lamésystem that will be satisfied between studied the far-field for elastic wave and the location and magnitude of the point sources into the loss function,constraining the reconstruction result of the data-driven part.The experimental results show that this model can solve the inverse source problem for elastic wave.Numerical experiments and model convergence analysis under noise and finite observation aperture conditions show that the model has a good reconstruction effect on the reconstruction of the location and magnitude of the point sources,and verifies the effectiveness,stability and robustness of the model.