Uncertainty Quantification for Machine Learning assisted Plasma Density Estimation for Low Temperature Plasmas

AI/ML models are increasingly being used in plasma diagnostics, such as for estimating plasma density and temperature. However, for ML-based approaches to be reliably implemented in real-life situations, it is crucial to provide estimates of prediction uncertainty alongside accuracy measures. We present a Deep Learning (DL) model enhanced with Monte Carlo Dropout for both density estimation and uncertainty quantification, where the electric field pattern generated by incident microwave scattering from plasma is used to estimate density profiles in low-temperature collisional plasmas [1]. Training data has been generated using simulations that replicate real-life experimental scenarios. We focus on understanding and reliably quantifying uncertainty under various conditions by altering plasma density profiles, peak plasma densities, and setup for collecting scattered field data used to train and test the DL model. We observe, aleatoric uncertainty remains constant across different dataset sizes, indicating inherent data variability. In contrast, epistemic uncertainty decreases with increased data size but increases for out-of-distribution data points. Outliers on lower/upper limits exhibit much higher epistemic uncertainty.  Aleatoric uncertainty, attributed to inherent variability and noise in data, significantly impacts plasma density estimation, especially in scenarios involving asymmetric density profiles.

[1] Ghosh et al 2024 J. Phys. D: Appl. Phys. 57 014001.