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"NAME_1's equation plays an important role in the modeling of many physical systems. In electrostatic self-consistent low-temperature plasma (LTP) simulations, NAME_1's equation is solved in every simulation time step, which can amount to a significant computational cost of the whole simulation. In this paper, we describe the development of a generic machine-learned NAME_1 solver specifically designed for LTP simulations in complex 2D geometries, i.e., the reactors may include inner electrodes and dielectric materials. The approach utilizes a hybrid CNN-transformer network architecture combined with a weighted multiterm loss function. We train the network using highly-randomized synthetic data to ensure the generalizability of the trained network to unseen reactor geometries. The trained model demonstrates the ability to produce accurate solutions both in terms of quantitative and qualitative accuracy. Furthermore, it generalizes well on new reactor geometries such as reference geometries found in the literature. To increase the numerical reliability of the solutions, we employ a traditional solver to refine the raw predictions, especially to recover the high-frequency features unresolved by the model. Using this approach, one can arrive at reasonable solution accuracy that is still a couple of times faster than using a GPU-based traditional solver alone."

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