Stochastic gradient descent for optimization for nuclear systems

The use of gradient descent methods for optimizing k-eigenvalue nuclear systems has been shown to be useful in the past, but the use of k-eigenvalue gradients have proved computationally challenging due to their stochastic nature. ADAM is a gradient descent method that accounts for gradients with a stochastic nature. This analysis uses challenge problems constructed to verify if ADAM is a suitable tool to optimize k-eigenvalue nuclear systems. ADAM is able to successfully optimize nuclear systems using the gradients of k-eigenvalue problems despite their stochastic nature and uncertainty. Furthermore, it is clearly demonstrated that low-compute time, high-variance estimates of the gradient lead to better performance in the optimization challenge problems tested here.

Automated summary

This analysis investigates the suitability of ADAM as a tool for optimizing k-eigenvalue nuclear systems, using challenge problems to verify its effectiveness. Despite the stochastic nature and uncertainty of k-eigenvalue problems, ADAM is able to successfully optimize nuclear systems. Furthermore, the results clearly demonstrate that low-compute time, high-variance estimates of the gradient lead to better performance in the optimization challenge problems tested here.