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abstract: |
    Strongly gravitational lensing systems (SGL) encodes cosmology information in source/lens distance ratios $\mathcal{D}_{\rm
    obs}=\mathcal{D}_{\rm ls}/\mathcal{D}_{\rm s}$, which can be used to precisely constrain cosmological parameters. In this paper, based on future measurements of 390 strong lensing systems from the forthcoming LSST survey, we have successfully reconstructed the distance ratio $\mathcal{D}_{\rm obs}$ (with the source redshift $z_s\sim 4.0$), directly from the data without assuming any parametric form. A recently developed method based on model-independent reconstruction approach, Gaussian Processes (GP) is used in our study of these strong lensing systems. Our results show that independent measurement of the matter density parameter ($\Omega_m$) could be expected from such strong lensing statistics. More specifically, one can expect $\Omega_m$ to be estimated at the precision of $\Delta\Omega_m\sim0.015$ in the concordance $\Lambda$CDM model, which provides comparable constraint on $\Omega_m$ with Planck 2015 results. In the framework of the modified gravity theory (DGP), 390 detectable galactic lenses from future LSST survey would lead to stringent fits of $\Delta\Omega_m\sim0.030$. **Finally, we have discussed three possible sources of systematic errors (sample incompleteness, the determination of length of lens redshift bin, and the choice of lens redshift shells), and quantified their effects on the final cosmological constraints. 