Development of high-fidelity and fast-running surrogate models in support of the UT Austin project on the digital twins for MSRs
Task 1: Creation and calibration of a full order model of the MSRR
In this task Texas A&M University (TAMU) will create a full-order model of the Molten Salt Research Reactor (MSRR) based on the GeN-Foam multi-physics code [1].
GeN-Foam will be used to provide a 3-D representation of the primary circuit. For thermal-hydraulics, we will make use of a porous-medium approach to model geometrically repetitive and complex components like core and heat exchangers. Other components, including pipes and plena will be modeled using standard CFD RANS or LES turbulence models. If solid components exist that require explicit modeling of heat diffusion, this will be performed based on the GeN-Foam thermo-mechanical sub-solver, as well as coupled boundaries to connect them with the fluid and porous regions.
For neutronics, we will pursue various options amongst the following:
- Diffusion for both steady-state and transient, including if needed the use of super-homogenization or discontinuity factors;
- SP3 for both steady-state and transient, including the use of super-homogenization or discontinuity factors;
- SN for steady-state;
- Direct coupling with the Serpent2 Monte Carlo code for steady-state;
- Point kinetics with neutron importance and power shaped derived from spatial solutions.
Delayed neutron precursor diffusion and transport will be included in the model.
The effect of thermal deformations will be included via parametrization of cross-sections in spatial models and feedback coefficients for point-kinetics. GeN-Foam is capable of directly evaluating deformations and feeding them to the neutronics for mesh deformation. The model will be prepared to enable inclusion of this feature in the future.
During the project, the GeN-Foam model will be calibrated based on results obtained by the University of Texas at Austin (UT) using the VERA toolsuite.
Substasks:
- Geometry and mesh creation,
- Performance of sanity checks,
- Thermo-hydraulics modeling,
- Neutronics modeling,
- Multiphysics modeling,
- Model calibration.
Task 2: Creation of a reduced order model of the MSRR
Fast surrogate models for parametric multiphysics applications can enable near real-time response with controllable accuracy. Such models can aid in many standard engineering tasks, such as design optimization, sensitivity studies, and uncertainty quantification. In addition, surrogate models can be incorporated into Digital Twins (DTs), where future predictions or forensics analysis of past situations are needed. The parametric aspect of such surrogate models is crucial for deployment in DTs as the models need to be adaptable (or learn) from sensor data, once such data becomes available.
For future DT application of the MSRR, we will develop surrogate models based on the traditional “modeling and simulation” practice, i.e., using engineering-grade software to learn the typical dynamics of simulations of interest, under parametric variation, followed by model-order reduction to learn from these higher-order (and most expensive) simulations in order to enable near real-time responses.
In this proposed work, we focus on physics-based surrogate modeling, such as PDE-based reduced-order modeling. Recently, we developed and demonstrated the performance of projection-based (i.e., intrusive) model-order reduction for multiphysics application for Molten Salt Reactors, with several application examples dealing with the fast-spectrum MSFR system [2]. However, intrusive ROMs can be heavy to implement for general multiphysics applications, mostly due to the nonlinear terms arising from material properties and correlations. Based on our prior experience we believe that, in the longer term, non-intrusive model-order reduction approaches are more suitable, significantly less burdensome on the users (and the developers) for a marginal loss of accuracy.
The development of non-intrusive reduced-order models (NI-ROMs) is scalable across physics and we propose to demonstrate it using a multiphysics model of the MSRR reactor. The high-fidelity models from task-1, above, will be employed to generate the fast-running surrogate models in a non-intrusive manner.
NI-ROMs still rely on the learning of the subspace where the parametric family of multiphysic solutions live: this is typically achieved by exercising the high-fidelity (aka, full-order) model at points in the parameter space. This data-driven learning consists in compressing the full-order snapshot data to extract relevant basis functions. When POD/SVD is used for this, we talk about linear manifold learning; however, nonlinear learning via Variational AutoEncoders (VAEs) is a suitable alternative. The compression of the information leads to a much smaller set of unknowns, called the latent code. The latent code is at the heart of the reduced-order model. This process is schematically described in the figure below. The latent code, or expansion coefficients, are functions of the design/input parameters. For the training set, such latent code is readily available (as a by-product of the subspace learning/compression stage). In non-intrusive ROMs, a suitable functionalization of this latent is performed. Many options are available, including:
- Gaussian processes;
- Feedforward neural networks;
- Sparse grid interpolation.
Figure 1.: Principles of parametric model-order reduction.: first, in an “offline stage”, a certain number of solution snapshots, obtained for different parameter realizations, are collected. Then, the essence of the information gathered is extracted in the encoding step (learning stage), using SVD or auto-decoders, for instance. The latent code represents the model’s reduced coordinates in the learned manifold. The parametric dependence of the latent code can either be learned using non-intrusive approaches or can be obtained by projecting the full-order model equations into the learned subspace. Finally, knowledge of the latent code values enables the rapid reconstruction of the solutions. This final stage is the “online stage” and can be significantly faster than exercising the full-order model.
Substasks:
- Definition of parametric variations needed for the MSRR,
- Generation of snapshots using the high-fidelity model provided in task-1,
- Subspace learning for the multiphysics solution,
- Response hypersurface learning,
- Model calibration.
Task 3: Application to progression problems and demonstration
This task will be dedicated to supporting UT in the development of a set of progression problems that can be used to gradually check the capabilities of numerical models in simulating the steady-state and transient behavior of the MSRR and other MSRs.
Once the progression problem is defined, TAMU will: run the tools developed in Tasks 2 and 3 and compare results with those obtained by UT using VERA; calibrate the tools based on the outcome of the comparison (as part of Task 1).
Finally, TAMU will demonstrate the use of the models developed in Tasks 1 and 2 for the prediction of extrapolated states/designs of the MSRR.
Substasks:
- Definition of progression problems,
- Running of the tools for the progression problems and calibration,
- Demonstration of capabilities.
References
[1] Carlo Fiorina, Ivor Clifford, Manuele Aufiero, Konstantin Mikityuk, 2015. GeN-Foam: a novel OpenFOAM® based multi-physics solver for 2D/3D transient analysis of nuclear reactors, Nuclear Engineering and Design, Volume 294, 2015.
[2] German, P., Ragusa, J.C., Fiorina, C. and Retamales, M.T., 2019. Reduced-order modeling of parametrized multi-physics computations for the molten salt fast reactor. In International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C (pp. 1808-1817).