Cross Section Doppler Broadening prediction using Physically Informed Deep Neural Networks

Temperature dependence of the neutron-nucleus interaction is known as the Doppler broadening of the cross-sections. This is a well-known effect due to the thermal motion of the target nuclei that occurs in the neutron-nucleus interaction. The fast computation of such effects is crucial for any nuclear application. Mechanisms have been developed that allow determining the Doppler effects in the cross-section, most of them based on the numerical resolution of the equation known as Solbrig's kernel, which is a cross-section Doppler broadening formalism derived from a free gas atoms distribution hypothesis. This paper explores a novel non-linear approach based on deep learning techniques. Deep neural networks are trained on synthetic and experimental data, serving as an alternative to the cross-section Doppler Broadening (DB). This paper explores the possibility of using physically informed neural networks, where the network is physically regularized to be the solution of a partial derivative equation, inferred from Solbrig's kernel. The learning process is demonstrated by using the fission, capture, and scattering cross sections for $^{235}U$ in the energy range from thermal to 2250 eV.