Background <p>This study presents a novel stepped cavity with finite-length solid walls as a flow domain for micropolar nanofluids. The combined convection process is driven by heat conduction through the solid walls, while sinusoidal vibration is imposed within the flow region. The cavity is filled with an anisotropic porous medium characterized by irregular distributions of permeability, thermal conductivity, and Forchheimer coefficients.</p> Methods <p>The governing equations are solved using the Point-in-Polygon Finite Volume Method (PIP-FVM). In addition, stochastic deep neural network analysis is employed to evaluate the key thermal and concentration characteristics of the system.</p> Results <p>The results reveal that increasing the vibration frequency Ω from 100 to 500 reduces the temperature gradient and nanoparticle concentration gradient by 17.82% and 124.05%, respectively. Moreover, increasing the thickness of the plastic tile wall from 0.05 to 0.25 decreases the fluid Nusselt coefficient by 42.47%. The results also show that vibration promotes more uniform temperature and nanoparticle distributions within the cavity.</p> Originality/Value <p>The study demonstrates the effectiveness of imposed vibration as a practical control mechanism for enhancing heat and mass transfer uniformity in porous stepped cavities. It further highlights the significant role of conjugate wall material and thickness in determining thermal performance, showing that thicker low-conductivity walls substantially reduce the Nusselt number and improve thermal insulation.</p>