Optimization of the Woodcock Particle Tracking Method Using Neural Network

TL;DR

This paper introduces a neural network-based optimization of the Woodcock particle tracking method, significantly improving the figure of merit in 1D problems by adapting the sampling function q(x) using physics-informed neural networks.

Contribution

It proposes a novel neural network approach to optimize the Woodcock tracking parameter q(x), enhancing efficiency in particle transport simulations.

Findings

Significant FOM improvement in 1D Gaussian absorption case

Neural network effectively adapts q(x) for better sampling

Potential for extension to 3D voxel models

Abstract

The acceptance rate in Woodcock tracking algorithm is generalized to an arbitrary position-dependent variable $q(x)$. A neural network is used to optimize $q(x)$, and the FOM value is used as the loss function. This idea comes from physics informed neural network(PINN), where a neural network is used to represent the solution of differential equations. Here the neural network $q(x)$ should solve the functional equations that optimize FOM. For a 1d transmission problem with Gaussian absorption cross section, we observe a significant improvement of the FOM value compared to the constant $q$ case and the original Woodcock method. Generalizations of the neural network Woodcock(NNW) method to 3d voxel models are waiting to be explored.