Optimization of the Woodcock Particle Tracking Method Using Neural Network

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.