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低温等离子体的反问题是指根据等离子体的密度、电场等物理特性来反演电压幅值、频率等放电参数，反问题的求解是对等离子体进行智能控制的重要前提，在流体描述的框架下，基于传统的离散化方法来求解反问题往往是非常困难的。本文引入物理信息神经网络（Physics-Informed Neural Networks,PINNs）对大气压射频等离子体的反问题的进行求解，把连续性方程、泊松方程及漂移扩散近似等主要控制方程与作为待求解放电参数的电压幅值与频率，及额外的电场数据这三部分作为约束嵌入PINNs的损失函数中。经过训练后，PINNs可以实现对电压幅值与频率等放电参数的精确反演，且可以保证误差均在1%以内，同时也可以完整地输出密度、电场、通量等物理量的时空演化。为进一步优化额外数据对PINNs计算的影响，本文还深入分析了电场数据的采样位置、采样数量以及噪声水平对反演电压幅值与频率的效果。本研究表明，PINNs能够在给定实验或计算数据条件下，实现射频等离子体放电参数的精准反演及等离子体物理特性的精确计算，从而为推进对等离子体的智能控制打下基础。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 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 simultaneously 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 inversion of discharge parameters and accurate prediction of plasma characteristics under given experimental or computational data, thereby laying the foundation for intelligent control of low-temperature plasmas.
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Keywords:
- Low-temperature plasma 1 /
- Fluid model 2 /
- Machine learning 3 /
- PhysicsInformed Neural Networks (PINNs)4
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