# PHYSICS-INFORMED NEURAL NETWORK SOLUTION OF POINT KINETICS EQUATIONS FOR PUR-1 DIGITAL TWIN

A *digital twin* (DT), which keeps track of nuclear reactor history to provide real-time predictions, has been recently proposed for nuclear reactor monitoring. A digital twin can be implemented using either a differential equations-based physics model, or a data-driven machine learning model**. **The principal challenge in physics model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, while the main challenge in data-driven DT appears in the extensive training requirements and potential lack of predictive ability.

In this thesis, we investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. In this way, PINNs establish theoretical constraints and biases to supplement measurement data and provide solution to several limitations of purely data-driven machine learning (ML) models. We develop a PINN model to solve the point kinetic equations (PKEs), which are time dependent stiff nonlinear ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring the spatial dependence of the neutron flux. PKEs portray the kinetic behavior of the system, and this kind of approach is the basis for most analyses of reactor systems, except in cases where flux shapes are known to vary with time. This system describes the nuclear parameters such as neutron density concentration, the delayed neutron precursor density concentration and reactivity. Both neutron density and delayed neutron precursor density concentrations are the vital parameters for safety and the transient behavior of the reactor power.

The PINN model solution of PKEs is developed to monitor a start-up transient of the Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The facility under modeling, PUR-1, is a pool type small research reactor located in West Lafayette Indiana. It is an all-digital light water reactor (LWR) submerged into a deep-water pool and has a power output of 10kW. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation.

The findings of this thesis research indicate that the PINN model achieved highest performance and lowest errors in data interpolation. In the case of extrapolation data, three different test cases were considered, the first where the extrapolation is performed in a five-seconds interval, the second where the extrapolation is performed in a 10-seconds interval, and the third where the extrapolation is performed in a 15-seconds interval. The extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

## Funding

### U.S. Department of Energy, Advanced Research Projects Agency - Energy (ARPA-E) Generating Electricity Managed by Intelligent Nuclear Assets (GEMINA) program under Contract DE-AC02-06CH11357

## History

## Degree Type

- Master of Science

## Department

- Nuclear Engineering

## Campus location

- West Lafayette