Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics

The paper presents a novel approach based on Physics-Informed Neural Networks (PINNs) for the solution of Point Kinetics Equations (PKEs) with temperature feedback. The approach is based on a new framework developed by the authors, which combines PINNs with Theory of Functional Connections and Extreme Learning Machines in the so called Extreme Theory of Functional Connections (X-TFC). The accuracy of X-TFC is tested against a number of published benchmarks (including for non-linear PKEs), showing its performance both in terms of accuracy and computational time. One of the main advantages of the proposed framework is in its flexibility to adapt to a variety of problems with minimal changes in coding and, after the training of the network, in its ability to offer an analytical representation (by Neural Networks) of the solution at any desired time instant outside the initial discretization.