Item identification with a space-dependent model of neutron multiplicities and artificial neural networks

A method of calculating the neutron multiplicity rates (singles, doubles and triples rates), based on transport theory, was developed by us recently. The model treats the full 3-D spatial transport and multiplication of neutrons, accounting also for the shape of the item and the spatial distribution of the source, in one-speed theory. For a given item and its source distribution, the model can predict the multiplicity rates more precisely than the point model, on which traditional neutron multiplicity counting is based. However, so far it has not been investigated how the enhanced accuracy of the calculated multiplicity rates (i.e. the solution of the direct task) can be used to estimate the parameters of interest of the measurement item, primarily the fission rate (the solution of the inverse task). Unlike for the point model, the multiplicity rates under the extended scheme can only be given numerically, as solutions of integral transport equations, and hence an analytical inversion of the formulae is not possible. In this work it is investigated how machine learning methods, primarily the use of artificial neural networks, which only need numerical values of the solution of the direct task (the multiplicity rates), can be used for this purpose. It is shown that for numerical test items containing a mixture of 239Pu and 240Pu, the fraction of the latter varying between 4% and 25%, one can extract the masses of both isotopes from a properly trained network.