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Sub-wavelength diffractive optics, commonly known as meta-optics, present a complex numerical simulation challenge, due to their multi-scale nature. The behavior of constituent sub-wavelength scatterers, or meta-atoms, needs to be modeled by full-wave electromagnetic simulations, whereas the whole meta-optical system can be modeled using ray/ Fourier optics. Most simulation techniques for large-scale meta-optics rely on the local phase approximation (LPA), where the coupling between dissimilar meta-atoms is neglected. Here we introduce a physics-informed neural network, coupled with the overlapping boundary method, which can efficiently model the meta-optics while still incorporating all of the coupling between meta-atoms. We demonstrate the efficacy of our technique by designing 1mm aperture cylindrical meta-lenses exhibiting higher efficiency than the ones designed under LPA. We experimentally validated the maximum intensity improvement (up to 53%) of the inverse-designed meta-lens. Our reported method can design large aperture ( ~ 10⁴ − 10⁵λ) meta-optics in a reasonable time (approximately 15 minutes on a graphics processing unit) without relying on the LPA.