Research On Machine Learning Method For Solving A Class Of Acoustic Inverse Scattering Problems

The inverse scattering problem is a typical inverse problem of mathematical physics,which is widely used in petroleum exploration,medical imaging and other fields.Therefore,the research on the inverse scattering problem has important scientific significance and practical value.This thesis mainly studies a type of acoustic inverse scattering problem: given the incident wave and the measured far-field information,reconstruct the boundary shape of the unknown scatterer.Numerical solutions of such problems usually encounter the difficulties of nonlinearity and ill-posedness.In particular,the observational information in practical problems often has inevitable lack of data,which makes the effective solution of inverse scattering problems extremely challenging.In recent years,with the development of machine learning technology,this technology is widely used in image processing,geological exploration and other fields.Machine learning is a data-driven computing technology,which can compensate for the lack of data in traditional algorithms to some extent,so machine learning is widely used in inverse problems.This thesis will discuss and analyze the acoustic inverse scattering problems based on machine learning technology.The following problems are discussed:Firstly,the mathematical expression of the dataset constructed by cubic spline interpolation function approximating the boundary of scatterer is given.Secondly,through the artificial neural network model,the Fourier method and cubic spline method are used to construct dataset respectively to carry out numerical inversion for a single scatterer.By calculating the relative error between the inversion results and the true boundary shape of the scatterer,the comparison results between the inversion results obtained by the two methods and the true boundary shape of the scatterer are obtained.At the same time,it is found that the machine learning method is also effective for the inversion of single scatterer with sound-hard boundary conditions.Thirdly,taking the dataset constructed by the Fourier method as an example,it is found that the machine learning method is also effective for the inversion of multiple scatterers,and the inversion results of two scatterers under different boundary conditions,distances and scales are compared by the relative error between the inversion results and the true boundary of scatterers.It is numerically verified that the machine learning method is effective for the above problems.Finally,the inversion of the limited-aperture and phaseless data problem are discussed,it is numerically verified that the machine learning method is effective for the problems lack of data.