With full-field imaging and high photon efficiency advantages, structured illumination microscopy (SIM) is one of the most potent super-resolution (SR) modalities in bioscience. Regarding SR reconstruction for SIM, spatial domain reconstruction (SDR) has been proven to be faster than traditional frequency domain reconstruction (FDR), facilitating real-time imaging of live cells. Nevertheless, SDR relies on high-precision parameter estimation for reconstruction, which tends to suffer from low signal-to-noise ratio (SNR) conditions and inevitably leads to artifacts that seriously affect the accuracy of SR reconstruction. In this Letter, a physics-enhanced neural network-based parameter-free SDR (PNNP-SDR) is proposed, which can achieve SR reconstruction directly in the spatial domain. As a result, the peak-SNR (PSNR) of PNNP-SDR is improved by about 4 dB compared to the cross-correlation (COR) SR reconstruction; meanwhile, the reconstruction speed of PNNP-SDR is even about five times faster than the fast approach based on principal component analysis (PCA). Given its capability of achieving parameter-free imaging, noise robustness, and high-fidelity and high-speed SR reconstruction over conventional SIM microscope hardware, the proposed PNNP-SDR is expected to be widely adopted in biomedical SR imaging scenarios.