Physics-informed machine learning (ML) techniques are being developed and applied to existing computational tools, e.g. the System Analysis Module (SAM) developed at Argonne, to create a computationally efficient analysis framework for nuclear reactor design and analysis.

Results

Although the main objective of a system-level code is to conduct whole-plant transient analysis, three-dimensional (3D) simulation capability is still desirable to tackle complex thermal-fluid (T-F) phenomena in advanced reactors (e.g., mixing and thermal stratification phenomena in large pools or enclosures). SAM is currently developing a 3D module to accurately model complex T-F phenomena. This module adopts a coarse mesh setup to be consistent with the one-dimensional system modeling framework, which ensures computational efficiency.

We are investigating a novel data-driven approach that utilizes fine mesh Computational Fluid Dynamics (CFD) data to develop a coarse mesh closure relation for SAM. State-of-the-art deep learning technologies are applied for modeling 3D reactor T-F phenomena. Current study is focusing on applying convolutional neural networks (application: Dense-3D) and recurrent neural networks (application: POD-LSTM) for turbulence prediction in reactor transient. The two neural network models have been used for turbulence prediction during a loss-of-flow transient. The current results shown in the figure indicate that both neural network models have reasonably good agreement with the original CFD data. Such an observation confirmed the potential of applying deep learning technologies to support coarse mesh 3-D module development in SAM.

The two neural network models have been used for turbulence prediction during a loss-of-flow transient. The current results showed that both neural network models have reasonably good agreement with the original CFD data. Such an observation confirmed the potential of applying deep learning technologies to support coarse mesh 3-D module development in SAM.

An ongoing task is the uncertainty quantification (UQ) for the ML model in SAM. An inverse UQ approach that is based on Kalman filtering and supported by high-fidelity simulation results (e.g. large eddy simulation from Nek5000) or experimental measurements is under investigation is shown in the figure. The major advantage of the proposed approach is it considers the UQ approach within the physics solver (i.e. SAM), thus ensures the physical constrains, including mass/momentum/energy conservation of the obtained uncertainty results.

A preliminary study on a steady state bubbly flow simulation case confirmed the applicability of the proposed approach. In the case study, the uninformed prior uncertainty converged to the posterior uncertainty with the provided experimental measurements after 15 Kalman iterations.

Challenges

The method and lessons-learned employed in this work will potentially be applied to other phenomena and engineering applications, as physics-guided data-driven ML is expected to be a critical path for Argonne and DOE to move toward truly predictive multi-scale modeling.