  In practical engineering experiments, the data obtained through detectors are
inevitably noisy. For the already proposed data-enabled physics-informed neural
network (DEPINN) \citep{DEPINN}, we investigate the performance of DEPINN in
calculating the neutron diffusion eigenvalue problem from several perspectives
when the prior data contain different scales of noise. Further, in order to
reduce the effect of noise and improve the utilization of the noisy prior data,
we propose innovative interval loss functions and give some rigorous
mathematical proofs. The robustness of DEPINN is examined on two typical
benchmark problems through a large number of numerical results, and the
effectiveness of the proposed interval loss function is demonstrated by
comparison. This paper confirms the feasibility of the improved DEPINN for
practical engineering applications in nuclear reactor physics.

Machine Learning;Data Analysis, Statistics and Probability