CSST Strong Lensing Preparation: Fast Modeling of Galaxy-Galaxy Strong Lenses in the Big Data Era

Galaxy-galaxy strong lensing provides a powerful probe of galaxy formation, evolution, and the properties of dark matter and dark energy. However, conventional lens-modeling approaches are computationally expensive and require fine-tuning to avoid local optima, rendering them impractical for the hundreds of thousands of lenses expected from surveys such as Euclid, CSST, and Roman Space Telescopes. To overcome these challenges, we introduce TinyLensGPU, a GPU-accelerated lens-modeling tool that employs XLA-based acceleration with JAX and a neural-network-enhanced nested sampling algorithm, nautilus-sampler. Tests on 1,000 simulated galaxy-galaxy lenses demonstrate that on an RTX 4060 Ti GPU, TinyLensGPU achieves likelihood evaluations approximately 2,000 times faster than traditional methods. Moreover, the nautilus-sampler reduces the number of likelihood evaluations by a factor of 3, decreasing the overall modeling time per lens from several days to roughly 3 minutes. Application to 63 SLACS lenses observed by the Hubble Space Telescope recovers Einstein radii consistent with the literature values (within $\lesssim 5\%$ deviation), which is within known systematic uncertainties. Catastrophic failures, where the sampler becomes trapped in local optima, occur in approximately 5\% of the simulated cases and 10\% of the SLACS sample. We argue that such issues are inherent to automated lens modeling but can be mitigated by incorporating prior knowledge from machine learning techniques. This work thus marks a promising step toward the efficient analysis of strong lenses in the era of big data. The code and data are available online: https://github.com/caoxiaoyue/TinyLensGpu.