Advancing Stochastic Modelling for Safer Nuclear Reactor Operations

The MaThRad team is working to improve stochastic modelling in low-population reactor physics, tackling critical challenges in reactor start-up, shutdown, waste management, and nuclear security.

When neutron populations are extremely low, traditional deterministic models break down, making it crucial to account for stochastic fluctuations. In reactor start-up, for example, the system can either experience a sudden power surge or neutron extinction—understanding these probabilities is key to ensuring safe operations.

Existing approaches, like the Pál-Bell backward equation, have been successful but struggle with certain complex scenarios, such as randomly varying media. This work takes a fresh approach:

🔹 Martingale-based stochastic modelling to describe neutron and precursor population dynamics

🔹 Diffusive approximations leading to stochastic differential equations (SDEs)

🔹 Efficient PDE formulation to statistically describe the system while reducing reliance on computationally expensive Monte Carlo simulations

By leveraging insights from probability theory, the team aims to develop models that enhance safety and efficiency in nuclear reactor operations.

Next steps? The team will present this latest research “The Effect of Negative Sample Paths on the Accuracy of Numerical Solutions for Stochastic Point-Kinetics,” at the American Nuclear Society International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2025)