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The inverse problem of low-temperature plasmas refers to determining discharge parameters such as voltage amplitude and frequency from plasma characteristics, including plasma density, electric field and electron temperature. Within the framework of fluid description, it is usually very challenging to address inverse problems by using traditional discretization methods. In this work, physics-informed neural networks (PINNs) are introduced to solve the inverse problem of atmospheric-pressure radio-frequency plasmas. The loss function of the PINNs is constructed by embedding three components: the main governing equations (continuity equation, Poisson equation, and drift–diffusion approximation), the discharge parameters to be inferred (voltage amplitude and frequency in this study), and additional electric field data. The well-trained PINNs can accurately recover the discharge parameters with errors within about 1%, while providing the full spatiotemporal evolution of plasma density, electric field, and flux. Furthermore, the effects of sampling positions, sampling sizes, and noise levels of the electric field data on the inversion accuracy of voltage amplitude and frequency are systematically investigated. The results demonstrate that PINNs are capable of achieving precise inversions of discharge parameters and accurate prediction of plasma characteristics under given experimental or computational data, thereby laying a foundation for the intelligent control of low-temperature plasmas.
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Keywords:
- low-temperature plasma /
- fluid model /
- machine learning /
- physics-informed neural networks
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] -
数据集 采样点位置 幅值$ {\hat V_0} $ 幅值相对误差/% 频率$ \hat f $ 频率相对误差/% 1 $E(0, t)$ 435.83 0.94811 10.046 0.46051 2 $E\left(\dfrac{1}{4}d, t\right)$ 434.03 1.3559 9.981 0.18646 3 $E\left(\dfrac{1}{2}d, t\right)$ 431.73 1.88 10.023 0.23 4 $E\left(\dfrac{3}{4}d, t\right)$ 432.65 1.67 10.015 0.15 5 $E(d, t)$ 437.01 0.68 10.010 0.099 6 $E(x, 0)$ — — — — 7 ${N_{\text{e}}}\left(\dfrac{1}{2}d, t\right) + {N_{\text{i}}}\left(\dfrac{1}{2}d, t\right)$ — — — — 
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数据集 采样点数量 幅值$ {\hat V_0} $ 幅值
相对误差/%频率$ \hat f $ 频率
相对误差/%1 200 436.27 0.847 10.010 0.10 2 150 437.50 0.569 10.011 0.12 3 100 437.01 0.679 10.011 0.10 4 50 436.83 0.720 10.013 0.13 5 30 436.21 0.860 10.011 0.11 6 20 434.92 1.154 10.010 0.10 7 10 429.58 2.368 10.019 0.19
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数据集 噪声
水平幅值
$ {\hat V_0} $/V幅值
相对误差/%频率$ \hat f $
/MHz频率
相对误差/%1 0.01 438.34 0.378 10.010 0.098 2 0.02 438.48 0.345 10.008 0.078 3 0.04 439.37 0.144 10.002 0.021 4 0.06 439.78 0.051 10.009 0.092 5 0.08 434.44 1.263 9.934 0.646 7 0.1 432.09 1.797 9.915 0.850 8 0.12 428.05 2.716 9.8873 1.127
DownLoad: CSV
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35]
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