Machine Learning-Based Bias Correction for the GEIM Model

This study focuses on real-time reconstruction of the spatial distribution of nuclear power using limited measurement observations. While physical models, such as the generalized empirical interpolation method (GEIM), can reconstruct the spatial field, they often cause bias if the model used to construct it is biased. The parametrized background data weak (PBDW) method attempts to mitigate this model bias, but its effectiveness is limited. To improve model bias correction, this paper proposes leveraging machine learning techniques-specifically, support vector regression, ${\rm K}$-nearest neighbors, and decision trees to enhance the GEIM method. These techniques predict model bias distributions across the entire field based on observed model bias at measurement points. The results demonstrate that Gaussian process based correction performs comparably to PBDW, both offering superior accuracy and robustness against noise, while other machine learning methods exhibit instability under varying parameter settings.