A neural-network enhanced adaptive design for ultrathin, single-substrate polarization converters optimized for wideband transmission is proposed. This research utilizes machine learning to tackle the inverse design challenge, aiming for customizable relative bandwidths of polarization conversion up to 20%. The design incorporates only a dielectric layer surrounded by two metallic layers. A sophisticated concatenated network architecture is central to this work, inversely designing converters for the 10-16 GHz band and achieving targeted bandwidths of 10%-20% at various frequencies with transmission amplitudes exceeding 0.9. One sample has been constructed and measured. This structure enables 90° cross-polarization conversion with a transmission bandwidth of 20%, with an optimized thickness of just 0.09λ0. Validation tests on the prototype demonstrate less than 2% error, confirming the method's precision and its potential for broader applications in metamaterial and metasurface design.