We present the development of a data-driven, AI-based model of the Point Spread Function (PSF) that achieves higher accuracy than the current state-of-the-art approach, "PSF in the Full Field-of-View'' (PIFF). PIFF is widely used in leading weak-lensing surveys, including the Dark Energy Survey (DES), the Hyper Suprime-Cam (HSC) Survey, and the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). The PSF characterizes how a point source, such as a star, is imaged after its light traverses the atmosphere and telescope optics, effectively representing the "blurred fingerprint'' of the entire imaging system. Accurate PSF modeling is essential for weak gravitational lensing analyses, as biases in its estimation propagate directly into cosmic shear measurements -- one of the primary cosmological probes of the expansion history of the Universe and the growth of large-scale structure for dark energy studies. To address the limitations of PIFF, which constructs PSF models independently for each CCD and therefore loses spatial coherence across the focal plane, we introduce a deep-learning-based framework for PSF reconstruction. In this approach, an autoencoder is trained on stellar images obtained with the Hyper Suprime-Cam (HSC) of the Subaru Telescope and combined with a Gaussian process to interpolate the PSF across the telescope's full field of view. This hybrid model captures systematic variations across the focal plane and achieves a reconstruction error of $3.4 \times 10^{-6}$ compared to PIFF's $3.7 \times 10^{-6}$, laying the foundation for integration into the LSST Science Pipelines.
Cosmology is the scientific discipline that, through observations of light and other cosmic signals such as gravitational waves, cosmic rays, and the cosmic microwave background, investigates the origin, structure, evolution, and ultimate fate of the Universe Bridle et al. (2009); Liddle (2003). The development of cosmology has been marked by key debates and discoveries that gradually defined its scientific foundations.
A good example is the so-called “Great Debate” of 1920, in which Harlow Shapley and Heber Curtis discussed the scale of the cosmos. While Shapley argued that the Milky Way encompassed the entire Universe, Curtis maintained that spiral nebulae such as Andromeda were in fact independent galaxies Trimble (1995). This controversy was settled only a few years later, when Edwin Hubble measured the distance to Andromeda and revealed that the Universe extends far beyond the Milky Way. He also provided the first observational evidence for the expansion of the Universe, consistent with Georges Lemaître’s theoretical predictions from general relativity The Editors of Encyclopaedia Britannica (2025).
Later, Fritz Zwicky noted that the visible matter in galaxy clusters was insufficient to explain their dynamics, suggesting the existence of “dark matter,” a hypothesis that decades later received strong support from Vera Rubin’s study of galaxy rotation curves. At the end of the 20th century, Saul Perlmutter, Adam Riess, and Brian Schmidt discovered through observations of Type Ia supernovae that cosmic expansion is accelerating, introducing the concept of “dark energy.” Despite decades of research, the fundamental nature of both dark matter and dark energy remains one of the most profound open questions in cosmology.
As a result, modern cosmology recognizes that our Universe is dominated by dark energy, an unknown component driving the accelerated expansion of the cosmos, and dark matter, an invisible form of matter that interacts only through gravity. These components are not fully understood by modern science. In the case of dark matter, there is much evidence for its existence, suggesting that it may be a particle interacting gravitationally and, at most, weakly with other forces. However, it remains unknown which particle beyond the Standard Model could account for it. With respect to dark energy, its nature is entirely mysterious, and one of the most powerful observational probes to constrain it is weak gravitational lensing Bridle et al. (2009); Hobson, Efstathiou, and Lasenby (2006); Liddle (2003).
Gravitational lensing is the deflection of light rays from distant celestial objects caused by the curvature of spacetime induced by the presence of mass-energy distributions, analogous to the way light bends when it passes through different media. A gravitational lens is a localized concentration of mass and energy, such as a galaxy or a cluster of galaxies, that distorts and focuses the trajectory of light, similar to the action of an optical lens, producing observable effects such as changes in the apparent position, shape, or brightness of the background source Kilbinger (2015); Liddle (2003); Mandelbaum (2018);Plazas Malagón (2014). Because the lensing effect depends on the mass distribution of the deflector (the lens), a detailed study of gravitational lenses allows researchers to infer valuable information about the total mass of the lensing object, including both its visible and dark matter components Mandelbaum (2018).
Depending on the level of distortion produced in the observed image, gravitational lensing can be classified into different regimes. In extreme cases, known as strong gravitational lensing, multiple images of the same source or even complete Einstein rings can be observed. Conversely, when distortions are subtle and not directly visible in individual images, it is necessary to average over many background galaxies and apply statistical methods to detect the effect, a phenomenon referred to as weak gravitational lensing Mandelbaum (2018); Plazas Malagón (2014).
Weak lensing is used to measure cluster masses and perform cosmological studies. An even subtler effect is cosmic shear, which provides key insights into the large-scale distribution of matter in the Universe Amon and et al. (2022); Kilbinger (2015).
Cosmic shear is the subtle distortion in the shapes of galaxies. For most galaxies, this effect can be described as a linear transformation between unlensed (xu, yu) and lensed (x l , y l ) coordinates applied to the entire galaxy image
Here, a positive “shear” g 1 stretches an image along the x axis and compresses along the y axis; a positive shear g 2 stretches an image along the diagonal y = x and compresses along y = -x Bridle et al. (2009).
These distortions tend to align galaxy shapes perpendicular to the center of the dark matter overdensity that bends the light. Since this effect is extremely small, it cannot be detected in an individual galaxy; therefore, a sta
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