Physics-informed machine learning typically assumes that the underlying physical laws are known and abundant training data is available. These assumptions do not hold in the context of self-organization of matter, a phenomenon that leads to the emergence of patterns when a surface is irradiated with an ultrafast laser beam. Indeed, due to the constraints of the electronic data acquisition devices, the creation of large datasets is made impossible. Moreover, modeling this dynamic process is challenging as it involves coupling between electromagnetism, thermodynamics and fluid mechanics under far-from-equilibrium conditions that are not yet fully understood. This paper aims at taking a step forward towards a better understanding of this complex phenomenon. We specifically focus on the laser energy absorption of the surface, which is governed by the distinctive characteristics of Maxwell's equations in an inhomogeneous lossy medium. This involves modelling physics at the nano scale and incurs high simulation costs that make any exploration impractical. To address this major issue, we investigate different physics-informed learning models. In this low data regime, our study reveals that learning a simple U-Net-based surrogate model surpasses (i) more sophisticated neural architectures and (ii) the FDTD-based solver in speed by several orders of magnitude. Interestingly, our study highlights a link between the formation of patterns and the magnitude of absorbed energy.