  Driven by human ingenuity and creativity, the discovery of super-resolution
techniques, which circumvent the classical diffraction limit of light,
represent a leap in optical microscopy. However, the vast space encompassing
all possible experimental configurations suggests that some powerful concepts
and techniques might have not been discovered yet, and might never be with a
human-driven direct design approach. Thus, AI-based exploration techniques
could provide enormous benefit, by exploring this space in a fast, unbiased
way. We introduce XLuminA, an open-source computational framework developed
using JAX, which offers enhanced computational speed enabled by its accelerated
linear algebra compiler (XLA), just-in-time compilation, and its seamlessly
integrated automatic vectorization, auto-differentiation capabilities and GPU
compatibility. Remarkably, XLuminA demonstrates a speed-up of 4 orders of
magnitude compared to well-established numerical optimization methods. We
showcase XLuminA's potential by re-discovering three foundational experiments
in advanced microscopy. Ultimately, XLuminA identified a novel experimental
blueprint featuring sub-diffraction imaging capabilities. This work constitutes
an important step in AI-driven scientific discovery of new concepts in optics
and advanced microscopy.
