# On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem

arXiv: https://arxiv.org/abs/2303.08455 · HTML: https://mlsanity.com/paper/2303.08455/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 53 references that are in the map.
- First posted on arXiv 15 Mar 2023.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review](https://mlsanity.com/paper/1611.00740/) (2016)
- [The Convergence Rate of Neural Networks for Learned Functions of Different Frequencies](https://mlsanity.com/paper/1906.00425/) (2019)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach](https://mlsanity.com/paper/2002.02600/) (2020)
- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Unsupervised Neural Networks for Quantum Eigenvalue Problems](https://mlsanity.com/paper/2010.05075/) (2020)
- [Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems](https://mlsanity.com/paper/2209.11134/) (2022)
- [Data-driven modeling for boiling heat transfer: using deep neural networks and high-fidelity simulation results](https://mlsanity.com/paper/1808.01859/) (2018)

## Built on by (most cited first, 2 of 2)

- [Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint](https://mlsanity.com/paper/2409.00458/) (2024)
- [Artificial Intelligence in Reactor Physics: Current Status and Future Prospects](https://mlsanity.com/paper/2503.02440/) (2025)

## Abstract (arXiv)

In practical engineering experiments, the data obtained through detectors are inevitably noisy. For the already proposed data-enabled physics-informed neural network (DEPINN) citepDEPINN, 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.