Neural Network Domain Decomposition for Core Neuronics
Matthew Louis / May 2025 (280 Words, 2 Minutes)
Machine learning is an ever popular technique to solve problems that would be difficult if not impossible to develop deterministic mathematical algorithms for. A familiar pedogogical example is image classification - a problem so subjective it doesn’t even make sense to think of a determinsitic algorithm without reference to a given dataset (of image class pairs). This paradigm has been applied ad nauseam to a heriocally diverse set of problems, and has seen great success in scientific as well as non-scientifici domains. These techniques are gradually making their way to nuclear engineering modsim, but progress is slow, and the ground seems fertile for new ideas. In light of this, I wanted to try applying Mahcine learning to an interesting approach to reactor core neutronics: the incident flux response expansion.
This idea has been explored by Dr. Farzad Rahnema at Georgia Tech, but I haven’t seen it mentioned much outside his group despite the apparent technical merit. I’m not familiar enough with the actual implementation of this method in the current state of the art code, COMET, to say for sure, but one bottleneck I identified was the determinsitic tabulation of the reponse functions using expansion functions. Response functions must be computed for each assembly type at each burnup step, and are themselves a function of energy, space, and angle. These reponse functions are used to compute how the angular flux in each subdomain “responds” to a given incident flux (also expanded on some basis), and are fundamentally hard to represent. I’ve heard that these libraries can become very large for certain problems, making full-core cycle depletion calculations (of industry relevance) difficult.
For a class project in a Statistical Machine Learning class (ECE6254), as the title suggests, I tried replacing this entire determinstic reponse function library with a neural network. Now the response function is essentially the Green’s function for the given subdomain, but we only really need a finely resolved pin flux (enough to resolve spatial self-shielding) and the outgoing fluxes for the incident flux iteration: a reduced Green’s function that maps incidnet fluxes to outgoing fluxes plus pin fluxes. Unfortunately, there’s no nice way to formulate this problem deterministically, which is most likely why current approaches compute the entire Green’s function. As a paradigm for solving problems that are hard for deterministic methods, I decided to try out a data-driven operator learning approach.
Unfortunately, I wasn’t able to get any compelling results in the timeframe of this project (even on a very simple 2D pincell-level domain decomposition), but my writeup with all of the gory details is below for anyone who’s intersted in pursuing this further (and if you are, reach out because I’d love to chat), or if you’re just curious.
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