Observations of bright protoplanetary disks often show annular gaps in their dust emission. One interpretation of these gaps is disk-planet interaction. If so, fitting models of planetary gaps to observed protoplanetary disk gaps can reveal the presence of hidden planets. However, future surveys are expected to produce an ever-increasing number of protoplanetary disks with gaps. In this case, performing a customized fitting for each target becomes impractical owing to the complexity of disk-planet interaction. To this end, we introduce DPNNet (Disk Planet Neural Network), an efficient model of planetary gaps by exploiting the power of machine learning. We train a deep neural network with a large number of dusty disk-planet hydrodynamic simulations across a range of planet masses, disk temperatures, disk viscosities, disk surface density profiles, particle Stokes numbers, and dust abundances. The network can then be deployed to extract the planet mass for a given gap morphology. In this work, first in a series, we focus on the basic concepts of our machine learning framework. We demonstrate its utility by applying it to the dust gaps observed in the protoplanetary disk around HL Tau at $10$ au, $30$ au, and $80$ au. Our network predict planet masses of $80 , M_{rm Earth}$, $63 , M_{rm Earth}$, and $70 , M_{rm Earth}$, respectively, which are comparable to other studies based on specialized simulations. We discuss the key advantages of our DPNNet in its flexibility to incorporate new physics, any number of parameters and predictions, and its potential to ultimately replace hydrodynamical simulations for disk observers and modelers.
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