Bayesian neural networks for predicting tokamak energy confinement time with uncertainty quantification

Abstract Accurate estimation of the tokamak energy confinement time ( τ E ) is crucial for optimizing the operation and design of fusion devices. Traditional methods, such as the ITER scaling law, often lack predictive precision and provide limited uncertainty quantification. To address these limitations, we develop two Bayesian neural network (BNN) models: VIBNN and NUTSBNN. These models leverage variational inference (VI) and the No-U-Turn Sampler (NUTS), respectively, for posterior inference. Evaluations on the multi-machine ITPA global H-mode confinement database and individual datasets from JET, DIII-D, and ASDEX-Upgrade, both models outperform conventional methods in terms of accuracy and provide reliable uncertainty estimates. NUTSBNN achieves higher accuracy with an inference time of ∼3 s, making it suitable for offline analysis, while VIBNN provides faster inference ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mn>0.05</mml:mn> </mml:mrow> </mml:math> s), which is promising for real-time applications. These results highlight the potential of BNNs for accurate and interpretable confinement time predictions in fusion research.