Inverse problems are of wide and important applications in many areas such as radar and sonar, medical imaging, nondestructive testing and geophysical prospection. Inverse problems are ill-posed problems, so it is challenging to construct stable and highly effective inversion algorithms for them. One of the important methods to tackle this challenging issue is to devise an appropriate regularization strategy based on the a priori information of the unknown solution. The success of traditional regularization methods heavily depends on correctly encoding the a priori information of the unknown solution into the inversion algorithms, but this is in general very difficult in practical computation. With the development of deep learning techniques in recent years, it becomes possible to directly learn the a priori information of the unknown solutions of the inverse problems from data, which is helpful in developing highly effective and stable inversion algorithms. In this paper, we review some recent progres on inversion algorithms based on deep learning, focusing mainly on those based on learnable regularization framework. In addition, we also summarize the advantages and shortcomings of the inversion algorithms based on deep learning, and discuss their future research directions.

To date most studies of metallic nanowire are mainly focused on the atomistic mechanisms in tensile or compressive deformation, while little attention has been paid to the bending deformation behavior of nanowire. A full understanding of the bending properties of nanowire, however, can help improve the reliability and service life of nanodevices, particularly for the flexible and stretchable systems. In this work, we investigate the bending behavior of a NiAl nanowire on different loading conditions using molecular dynamics simulations. The NiAl nanowire under bending loads was shown to undergo elastic and plastic deformation. The bending modulus during elastic deformation was determined to be around 48.9 GPa, showing good agreement with the reported calculations. The plastic deformation, independent of temperature, strain rate and size, was produced by stress-induced martensitic transformation from B2 to L1₀ phases, leading to good bending ductility even under low temperature and high strain rate. Moreover, the NiAl nanowire exhibits superelasticity under bending with total recovery of deformation, which is driven by the reverse transformation from the L1₀ to B2 phases.