  We present GIGA-Lens: a gradient-informed, GPU-accelerated Bayesian framework
for modeling strong gravitational lensing systems, implemented in TensorFlow
and JAX. The three components, optimization using multi-start gradient descent,
posterior covariance estimation with variational inference, and sampling via
Hamiltonian Monte Carlo, all take advantage of gradient information through
automatic differentiation and massive parallelization on graphics processing
units (GPUs). We test our pipeline on a large set of simulated systems and
demonstrate in detail its high level of performance. The average time to model
a single system on four Nvidia A100 GPUs is 105 seconds. The robustness, speed,
and scalability offered by this framework make it possible to model the large
number of strong lenses found in current surveys and present a very promising
prospect for the modeling of $\mathcal{O}(10^5)$ lensing systems expected to be
discovered in the era of the Vera C. Rubin Observatory, Euclid, and the Nancy
Grace Roman Space Telescope.
