An approach based on a Physics-Informed Neural Network (PINN) is introduced to tackle the two-dimensional (2D) rheological consolidation problem in the soil surrounding twin tunnels with different cross-sections, under exponentially time-growing drainage boundary. The rheological properties of the soil are modelled using a generalized viscoelastic Voigt model. An enhanced PINN-based solution is proposed to overcome the limitation of traditional PINNs in solving integral-differential equations (IDEs) equations. In particular, two key elements are introduced. First, a normalization method is employed for the spatio-temporal coordinates, to convert the IDEs governing the consolidation problem into conditions characterized by unit-duration time and unit-area geometric domain. Second, a conversion method for integral operators containing function derivatives is devised to further transform the IDEs into a set of second-order constant-coefficient homogeneous linear partial differential equations (PDEs). By using the TensorFlow framework, a series of PINN-based models is developed, incorporating the residual adaptive sampling method to address the 2D consolidation equations of soft soils surrounding tunnels with different burial depths and cross-sections. Comparative analyses between the PINNbased solutions, and either finite element or analytical solutions highlight that the aforementioned normalization stage empowers PINNs to solve the PDEs across different spatial and temporal scales. The integral operator transformation method facilitates the utilization of PINNs for solving intricate IDEs.

In 1994, the bistatic radar sounding of the Moon was carried out from the Clementine spacecraft. Analysis of the measurement results showed that the intensity and polarization of the radio echo in a small region at the South Pole differed from the values typical of ordinary lunar soil, but were similar to those obtained from radar surveys of Greenland ice and Jupiter satellites. Thus, an assumption was made about the existence of water ice deposits in the lunar soil, which until now could neither be confirmed nor disproved. In 2023, the launch of the Russian Luna 26 orbiter is planned, on which a radar complex will be installed to conduct radar sounding of the Moon on megahertz waves. The main problem of bistatic observation of the Moon is the difficulty of determining the area that is involved in the formation of the reflected signal. Here we discuss the method of localizing the place of reflection of radio signals using the known ballistic parameters of a spacecraft and numerical simulation.