ZONA Technology proposes to develop an innovative nonlinear structural reduced order model (ROM) - nonlinear aerodynamic ROM methodology for the inflatable aeroelasticity of a clamped modeled ballute system. The proposed ROM-ROM methodology tightly couples a nonlinear-FEM based structural ROM with CFD based neural-net aerodynamic ROM to achieve a high computational efficiency. Indeed, the computing time for a typical wing flutter/LCO analysis is reduced from hours (direct) to minutes (ROM-ROM). The structural ROM enables a seamless time-integration of the ROM-ROM and could be coupled with other aerodynamic ROM methods like Volterra or POD. A time-accurate GasKinetic BGK method (BGKX) is adopted to generate the aerodynamic ROM for rarefied hypersonic unsteady aerodynamics/aeroelasticity applications to a ballute in atmospheric entry. With a natural boundary condition, BGKX is superior to continuum methods for unsteady flow simulations, and unified in transition to continuum flow regimes covering the peak dynamic pressure range in Earth/Martian entries. It can provide flow pressures and heat flux in one step. In Phase I, we will consider both a 2D membrane-on-wedge system and a modeled ballute system and investigate their static aeroelasticity as well as the feasibility/efficiency of the ROM-ROM approach for their dynamic aeroelastic responses (flutter/LCO). These capabilities are necessary for the development of inflatable aeroelasticity in NASA space program.