PTNO: Training Neural Operators with Noisy Monte Carlo Estimates for Particle Transport Problems

{'Problem': 'High-fidelity Monte Carlo (MC) simulations for particle transport problems are computationally expensive, creating a need for more efficient methods. This work addresses the gap in literature regarding the application of neural operators to reduce the computational burden associated with MC simulations, particularly in the context of noisy data and high variance in labels. The paper is a preprint and has not undergone peer review.', 'Method': "The authors propose the Particle Transport Neural Operator (PTNO) architecture, which leverages noisy, low-cost Monte Carlo labels for training. The method specifically addresses challenges such as high variance and high dynamic range in the labels. The loss function employed is the pointwise relative L2 loss (PRelL2), which is designed to optimize the model's performance in the presence of noisy data. The output layer utilizes a Softplus activation function to ensure positivity in the predictions. The training configuration includes a budget-allocation study that varies the number of training scenes (M), Monte Carlo samples per render (N), and independent renders per scene (K) to optimize the training process.", 'Results': 'PTNO demonstrates a neutron transport speedup of 10^4 to 10^5 times faster than converged Monte Carlo simulations. In terms of cost efficiency, PTNO is 10^3 to 10^5 times cheaper than MC at matched accuracy. For radiative transfer problems, the cost of MC at matched accuracy is reported to be 0.8 to 11 times as much as PTNO, indicating significant efficiency gains.', 'Limitations': 'The authors do not report any limitations in their work, and no obvious limitations are identified in the available text.', 'Why it matters': 'The implications of this work are substantial for downstream applications in particle transport and related fields, as PTNO provides a framework for significantly reducing the computational costs and time associated with high-fidelity simulations. This advancement could facilitate more extensive and complex simulations in real-time applications, enhancing the feasibility of using neural operators in practical scenarios.'}