Capacitively Coupled Argon Plasmas Fluid Simulations with Deep Learning Surrogates: Asymmetric Inference and Quantitative Trust Boundaries

Fluid simulations of capacitively coupled plasmas (CCP) are crucial for understanding their discharge physics, yet the high computational cost poses a major bottleneck. To overcome this limitation, we have developed a deep learning-based surrogate model designed to replicate the output of a onedimensional CCP fluid model with near-instantaneous inference speed. Through a systematic evaluation of three architectures—Feedforward Neural Network (FNN), Attention-enhanced Long Short-Term Memory network (ALSTM), and Convolutional-Transformer hybrid network (CTransformer)—we found that the sequence-structured ALSTM model achieves the optimal balance between speed and accuracy, with an overall prediction error of only 1.73% for electron density, electric field, and electron temperature in argon discharge. This study not only achieves simulation acceleration but also reveals that the model can accu- rately extrapolate from low-pressure conditions dominated by complex non-local effects to high-pressure conditions governed by simple local effects, whereas the reverse extrapolation fails. This phenomenon suggests that training under low-pressure conditions enables the model to capture more comprehensive data features. From the perspective of model weights, both low-pressure and high-pressure models assign key weights to the sheath region, but the low-pressure model exhibits higher weight peaks in the sheath, indicating a stronger ability to capture the key physical process of sheath dynamics. In contrast, the high-pressure model, due to its lower weights in the sheath region, may fail to adequately resolve the complex dynamics of the sheath when predicting new operating conditions, thereby limiting its ability for high-fidelity extrapolation. To ensure the reliability of this data-driven model in practical applications, we established a trust boundary of 5% normalized mean absolute spatial error for model performance through systematic extrapolation experiments. When the model’s extrapolation error falls below this threshold, the spatial distribution curves of predicted parameters such as electron density and electron temperature closely match the true physical distributions. However, once the error exceeds this critical point, systematic deviations such as morphological distortion and amplitude discrepancies begin to appear in the predicted spatial distributions, significantly diverging from the true physical laws. In the future, we will develop neural network models capable of processing high-dimensional spatial data and incorporating multi-dimensional input features such as various discharge gases, ultimately realizing a dedicated AI model for the field of capacitively coupled plasmas.