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Poisson's equation plays an important role in modeling many physical systems.In electrostatic self-consistent low-temperature plasma (LTP) simulations,Poisson's equation is solved at each simulation time step, which can amount toa significant computational cost for the entire simulation. In this paper, wedescribe the development of a generic machine-learned Poisson solverspecifically designed for the requirements of LTP simulations in complex 2Dreactor geometries on structured Cartesian grids. Here, the reactor geometriescan consist of inner electrodes and dielectric materials as often found in LTPsimulations. The approach leverages a hybrid CNN-transformer networkarchitecture in combination with a weighted multiterm loss function. We trainthe network using highly-randomized synthetic data to ensure thegeneralizability of the learned solver to unseen reactor geometries. Theresults demonstrate that the learned solver is able to produce quantitativelyand qualitatively accurate solutions. Furthermore, it generalizes well on newreactor geometries such as reference geometries found in the literature. Toincrease the numerical accuracy of the solutions required in LTP simulations,we employ a conventional iterative solver to refine the raw predictions,especially to recover the high-frequency features not resolved by the initialprediction. With this, the proposed learned Poisson solver provides therequired accuracy and is potentially faster than a pure GPU-based conventionaliterative solver. This opens up new possibilities for developing a generic andhigh-performing learned Poisson solver for LTP systems in complex geometries.

Towards a Machine-Learned Poisson Solver for Low-Temperature Plasma Simulations in Complex Geometries