Random Ray Methods
There are two broad paradigms in numerical analysis: the deterministic approach where space and/or time are discretised in order to approximate a dynamical system, and the Monte Carlo approach where the behaviour of the system is studied by simulating many random replicates of its evolution. The random ray method is a hybrid approach that seeks to leverage the advantages of both paradigms.
John Tramm presented a hybrid approach for nuclear reactors dubbed the “random ray method”. In this method, the characteristic lines are randomly simulated within the reactor, and solutions to discretised energy ODEs are computed along these lines. This method, which has been implemented in SCONE, produced astounding results. Firstly, the random ray method was measured to be 652 times faster than a standard deterministic solver. Secondly, the associated uncertainty was much more uniform than that obtained with pure Monte Carlo simulation.