Predicting radiation distribution via neural operator trained on basis function-generated data

The prediction of radiation-related quantity distributions through the solution of the transport equation is a computationally intensive process that necessitates substantial computational resources. Neural networks hold promise for rapid prediction; however, their utility is constrained by the scarcity of training datasets. In this study, we introduce a method using the Fourier Neural Operator (FNO) to predict radiation distributions, mitigating the challenges associated with limited datasets by generating data through basis functions. Our numerical experiments use the prediction of photon-deposited energy distributions in PET-CT examinations as an example. FNOs trained on datasets generated by basis functions show performance comparable to those trained on data derived from CT images. Specifically, the Mean Absolute Errors (MAEs) of FNOs trained on basis function-generated datasets are less than 65% of the MAEs of 3D U-Nets trained on CT images, which are commonly utilized for dose distribution prediction in the field of nuclear medicine. The inference time of FNOs is approximately 0.1 seconds, which is significantly quicker than the time taken for Monte Carlo simulations. Our findings underscore the generalization abilities of FNOs trained on basis function-generated data. This indicates a practical approach for the rapid prediction of radiation fields. Moreover, it suggests that the strategy of generating datasets using basis functions can effectively overcome the limitations caused by the scarcity of available datasets.