Application of data partitioned Kriging algorithm with GPU acceleration in real-time and refined reconstruction of three-dimensional radiation fields

Accurately assessing personal radiation doses in real radiation environments like nuclear power plants requires precise and real-time reconstruction of three-dimensional radiation fields. The Kriging algorithm, known for its accuracy in spatial interpolation, provides a promising approach for this task. However, its computational demands can be significant, especially in real-time scenarios. To address this, we enhance the Kriging algorithm with GPU acceleration and data partitioning strategies, enabling efficient and accurate reconstruction of three-dimensional nuclear radiation fields. Using Fluka software for Monte Carlo simulations, we generated a virtual radiation field of dimensions 5 m $\times$ 5 m $\times$ 5 m for a single-source, unshielded scenario, and a field of dimensions 20 m $\times$ 6 m $\times$ 8 m for a multi-source, shielded scenario. Using the simulated data, we compared the prediction accuracy of the improved algorithm with the conventional Kriging algorithm and further explored factors influencing the acceleration ratio of the improved algorithm. The results indicate that the GPU-accelerated and data-partitioned Kriging algorithm achieves nearly identical accuracy compared to the traditional method. In the single-source, unshielded scenario, with more than 343 known (measurement) points and predicting $95\times 95\times 95=$ 857,375 points, the prediction accuracy remains above 92.25%. In the multi-source, shielded scenario, with more than 8000 known (measurement) points and predicting $95\times 95\times 95=$ 857,375 points, the prediction accuracy remains above 91.17%. The acceleration performance of the improved algorithm is consistent across both scenarios, with the acceleration ratio increasing as the number of known and predicted points grows, reaching approximately 20 for smaller datasets and up to 93 for larger datasets. Additionally, the acceleration effect of the improved algorithm varies with data partition size, initially increasing and then decreasing as the partition size increases. When the number of known points is 512 and the number of predicted points is 884,736, the optimal partition size lies between 80,000 and 90,000, resulting in a prediction time of only 0.24 s.