This　letter　proposes　an　advanced　neural　space　mapping　(NSM)-based　inverse　modeling　method　and　its　applications　to　microwave　filter　design.　For　the　first　time,　the　NSM　method　is　introduced　into　inverse　microwave　modeling　with　input　dimensional　reduction　(IDR).　By　using　the　Fourier　transform　and　its　low-frequency　subspaces,　we　convert　the　S-parameter　curve　into　a　signal　spectrum　where　the　energy　is　concentrated　in　the　low-frequency　range,　to　reduce　the　dimension　of　the　inverse　model.　We　also　propose　a　two-stage　training　algorithm　for　the　NSM-based　inverse　model,　along　with　its　application　methodology　for　microwave　filter　design.　Two　microwave　filter　design　examples　are　presented　to　demonstrate　the　feasibility　of　the　proposed　method.　©　2024　IEEE.