Abstract
Liquid metal blankets plays a central role in future fusion reactors. Designing a new blanket or improving characteristics of a current blanket concept requires magnetohydrodynamic (MHD) codes to construct a suitable blanket solution. However, this often comes with an extremely high computational cost. Surrogate modeling is a modern approach which promises to mitigate this challenge by developing reliable, high-quality surrogates for MHD systems. Once trained, the surrogate models can be deployed to replace high-fidelity simulations, where the users can inquire directly to extract the system statistics and quantities of interest, virtually at no cost. In this work, we present an investigation and initial evaluation of three popular surrogate modeling methods for MHD flows in liquid metal fusion blankets, namely, sparse grid interpolation, sparse polynomial expansion and Gaussian process. These methods, which use interpolation or regression fits of high-fidelity simulations, are well-suited for the blanket problem, as they generally perform well with limited training data – a likely scenario given the cost of high-fidelity MHD simulations. We demonstrate the performance of surrogate modeling on a simple test case of fully-developed MHD flow in a rectangular duct, where the analytical solutions exist. For the MHD solutions on a fixed square domain with Hartmann number ranging from 100 to 10000 and wall conductivity ranging from 10−5 to 1, our results show that all three methods can construct surrogate models with relative errors less than 0.1%, using 200-600 simulations in training. Sparse grid outperforms sparse polynomial expansion and Gaussian process in term of accuracy, while the latter two approaches are more flexible in term of sampling locations. The insights and experience gained from this study are expected to serve as an important foundation for developing the approach to more practical and complex blanket applications.
| Original language | English |
|---|---|
| Article number | 115057 |
| Journal | Fusion Engineering and Design |
| Volume | 218 |
| DOIs | |
| State | Published - Sep 2025 |
Funding
We would like to thank Andrei Khodak (Princeton Plasma Physics Laboratory) for pointing out the closed-form formulae (2.3) and (2.4) for the analytical solutions to Hunt problem. This work was supported by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Fusion Energy Sciences programs, and accomplished at Oak Ridge National Laboratory (ORNL). ORNL is operated by UT-Battelle, LLC. for the U.S. Department of Energy under Contract DE-AC05-00OR22725. This material is based upon work supported by the U.S. Department of Energy, Office of Advanced Scientific Computing Research and Office of Fusion Energy Sciences; and was performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. De-AC05-00OR22725. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://www.energy.gov/doe-public-access-plan). We would like to thank Andrei Khodak (Princeton Plasma Physics Laboratory) for pointing out the closed-form formulae (2.3) and (2.4) for the analytical solutions to Hunt problem. This work was supported by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Fusion Energy Sciences programs, and accomplished at Oak Ridge National Laboratory (ORNL) . ORNL is operated by UT-Battelle, LLC., for the U.S. Department of Energy under Contract DE-AC05-00OR22725. This material is based upon work supported by the U.S. Department of Energy, Office of Advanced Scientific Computing Research and Office of Fusion Energy Sciences; and was performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. De-AC05-00OR22725. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( https://www.energy.gov/doe-public-access-plan ).
Keywords
- Fusion application
- Liquid metal MHD
- Surrogate modeling