Silicon photonics devices benefit greatly from a partially etched platform and inverse design. Herein, we propose a bi-layer polarization splitter and rotator with a topology pattern and demonstrate it on a silicon-on-insulator platform. Our device exhibits a significantly reduced physical footprint of only 2µm×6µm, compared to traditional directional couplers and tapered waveguides. The device accomplishes the functions of polarization conversion and separation in such a compact design without redundant tapered or bending waveguides. The tested minimum insertion loss with the fabrication batch reaches 0.57 and 0.67 dB for TE and TM modes, respectively. The TE mode demonstrates a wider bandwidth and lower ILs than the TM modes, averaging around 1 dB from 1530 to 1565 nm. The M modes exhibit approximately 2 dB ILs at the same wavelength range, decreasing to about 1 dB between 1565 and 1580 nm. Improved designs and fabrication conditions strongly suggest the potential for further performance enhancement in the device. This successful initiative validates the exceptional performance resulting from the integration of the partially etched platform and inverse design, providing valuable insights for future photonic integrated device designs.