Observations Regarding the Construction of Multipoint Kinetics Models from Observational Data

The multipoint kinetics (MPK) equations extend point kinetics models by tracking neutron populations in lumped reactor regions, offering improved spatial resolution at modest computational cost. However, determining the coupling coefficient matrix $K$ from transient data remains an open problem without established experimental procedures. This work provides some commentary on the task of recovering $K$ from observable forward flux measurements during reactor transients. Analytical solutions to the Kobayashi MPK formulation in the case of no precursors and with a single precursor family are derived in spectral form, enabling a mathematically rigorous investigation of eigenmode behavior and parameter observability. Coupling coefficient recoverability is investigated using modal sensitivity analysis and the Hessian condition number of the spectral recovery problem. The inclusion of delayed neutron precursors delays this eigenmode divergence but may be insufficient for enabling practical recovery of $K$ in many scenarios. In conclusion, capturing the behavior of nondominant eigenmodes without oversampling the dominant eigenmode is critical to the recoverability of $K$ through transient data.

K.G. Howey, Giorgio Valocchi, Dean Price · 2026