AI 中文总结
本研究开发PC-FDON模型，结合傅里叶增强分支、偏振条件分支与物理信息损失，从EFISH测量中重建电场，泛化性良好，可实现分布外检测，具等离子体外应用潜力。
AI 中文摘要
电场诱导二次谐波产生（EFISH）是一种成熟的激光诊断技术，用于量化等离子体中的电场，但由于信号具有相干性和路径积分特性，确保电场测量的准确性仍具挑战性。我们通过机器学习解决这一问题，开发了偏振条件傅里叶增强型深度算子网络（PC-FDON），这是一种统一的算子学习模型，可从两种偏振状态和不同光学参数下的EFISH测量中重建电场分布。其架构包含三项改进：（i）傅里叶增强分支，为古伊相位偏移和波矢失配提供归纳偏置；（ii）偏振条件分支，通过特征线性调制（FiLM）和门控单元编码信号偏振，使单个模型可处理两种偏振状态；（iii）物理信息损失，强制与EFISH控制方程自洽。在涵盖多个函数族、偏振状态和相位失配值的数据上训练后，PC-FDON在无噪声、不完整和有噪声输入下均实现了良好的重建效果，泛化能力与我们之前的偏振特定模型相当。通过蒙特卡洛dropout得到的逐点认知不确定性估计可反映模型置信度，并通过位置相关的超标分数指标实现分布外（OOD）检测。验证在两种偏振状态和不同瑞利范围下的真实电极配置上进行，包括模拟的表面介质阻挡放电，该框架正确标记了分布外输入，以及与模拟结果吻合良好的实验数据。该架构——频谱归纳偏置、条件调制和数据集特定不确定性——显示出超越等离子体诊断的更广泛应用潜力。
英文摘要
Electric-field-induced second-harmonic generation (EFISH) is an established laser diagnostic for quantifying electric fields in plasmas, yet ensuring field accuracy remains challenging given the coherent, path-integrated nature of the signal. We address this via machine learning, developing a Polarization-Conditioned Fourier-enhanced Deep Operator Network (PC-FDON) -- a unified operator-learning model that reconstructs field profiles from EFISH measurements across both polarizations and various optical parameters. Its architecture incorporates three advances: (i) a Fourier-enhanced branch providing inductive bias for the Gouy phase shift and wave-vector mismatch; (ii) a polarization-conditioning branch encoding signal polarization via Feature-wise Linear Modulation (FiLM) and gated units, enabling one model to handle both polarizations; and (iii) a physics-informed loss enforcing self-consistency with the governing EFISH equation. Trained on data spanning multiple function families, polarization states, and phase-mismatch values, PC-FDON achieves promising reconstruction under noise-free, incomplete, and noisy inputs, with generalizability comparable to our previous polarization-specific model. Pointwise epistemic uncertainty estimates via Monte Carlo dropout reflect model confidence and enable out-of-distribution (OOD) detection through a location-dependent exceedance fraction metric. Validation is performed on realistic electrode configurations under both polarizations and varying Rayleigh ranges, including a simulated surface dielectric barrier discharge where the framework correctly flags OOD inputs, and experimental data showing good agreement with simulations. The architecture -- spectral inductive bias, conditional modulation, and dataset-specific uncertainty -- shows strong potential for broader application beyond plasma diagnostics.
