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 investigate the adsorption mechanism of heavy oil on clay mineral surface during surfactant flooding, the microscopic mechanism of heavy oil and surfactant on montmorillonite surface under different temperatures can be explained by molecular dynamics simulation. Based on the four components (SARA) of heavy oil and sodium montmorillonite, the molecular dynamics simulation of the adsorption process is carried out after the water phase adsorbent containing surfactant molecules is added into the adsorption system. It shows that cationic surfactant tends to adsorb on the surface of montmorillonite and occupy more adsorption area, which makes the heavy oil molecules tend to separate from the surface of montmorillonite. The non-ionic surfactant does not show a tendency to adsorb towards the surface of montmorillonite during the relaxation process. Non-ionic surfactant has a high self-diffusion coefficient and thus diffuses in the adsorbent environment. High temperature disperses asphaltene aggregation nuclei in heavy oil, which facilitates heavy oil to flow away from the montmorillonite surface. However, high temperatures can also cause some surfactants more adhesion to the montmorillonite surface, resulting in surfactant loss. This study provides theoretical support for adjusting temperature and surfactant types during surfactant development and enhancing oil recovery of sensitive heavy oil reservoirs.

A hybrid particle-in-cell/fluid method is introduced to simulate the transport of intense ion beams in the solid plasmas. A two-dimensional numerical program opic2d-hybrid has been developed and it is used to study the collective behavior of the intense proton beam transport into the polyethylene and solid aluminum targets. It is shown that intense magnetic field is self-generated by the transport of intense proton beam in solid targets. This magnetic field is of benefit to pinch the proton beam. Moreover, due to the production of substantial free-electrons by the target heating and ionization, the stopping power of solid target become weaken, thereby lengthening the proton beam range. On the contrary, the increase of target temperature will reduce the resistivity and thus inhibit the generation of magnetic field. Furthermore, the target ionization leads to much stronger ion-ion scattering effect, thus resulting in the diffusion of protons in transverse space. These effects compete with each other and determine the transport behavior of intense proton beam. At the last, the physical factors contributing to the generation of magnetic field are also analyzed. Some means to increase the strength of magnetic field have been proposed in order to realize the pinch transport of intense proton beams in solid targets.

Targeting at SN algorithm for the neutron transport equation in the two-dimensional spherical coordinate system, we propose a directed graph model based on a (cell, direction) two-tuple, and design a multi-level parallel SN algorithm with controllable granularity on the basis of the existing parallel pipeline algorithm based on directed graph. Among them, a combination of domain decomposition and parallel pipeline is used to mine parallelism in the space-angle direction, and an energy group pipeline parallel method is proposed. Furthermore, by setting appropriate pipeline granularity, the overhead of scheduling, communication and idle waiting are well balanced. Experimental results show that the algorithm can effectively solve the neutron transport equation in the two-dimensional spherical coordinate system. For a typical neutron transport problem with 960 000 grids, 60 directions, 24 energy groups, and billions of degrees of freedom, the parallel program achieved 71% parallel efficiency on 1920 cores of a domestic parallel machine.