#34
Bayesian approach for validation of runaway electron simulations
Oral
Aaro Järvinen (VTT)
T. Fülöp, E. Hirvijoki, M. Hoppe, A. Kit, and J. Åström
Abstract
A Bayesian framework is implemented for validation of DREAM runaway electron simulations [1]. Validated predictive tools are required to optimize the scenarios and mitigation actuators in future fusion reactors to avoid the excessive damage that can be caused by unmitigated disruptions. Many of the simulation tools applied in fusion energy research require the user to specify several input parameters that are not explicitly constrained by the available experimental information. Hence, a typical validation exercise requires multiparameter optimization to calibrate the uncertain input parameters for the best possible representation of the investigated physical system. However, the conventional approach, where an expert modeler conducts the parameter calibration based on domain knowledge and previous experience, is prone to lead to an intractable validation challenge. For a typical simulation tool, conducting exhaustive multiparameter investigations manually to ensure a globally optimal solution and to rigorously quantify the uncertainties is an unattainable task, typically covered only partially and unsystematically. Fortunately, Bayesian inference algorithms offer a promising alternative approach that naturally includes uncertainty quantification as well as is less subjective to user bias in choosing the input parameters. The main challenge in using these methods is the computational cost of simulating enough samples to construct the posterior distributions for the uncertain input parameters. This challenge can be overcome by combining probabilistic surrogate modelling, such as Gaussian Process (GP) regression, with Bayesian optimization, which can reduce the number of required simulations by several orders of magnitude [2, 3]. In this project, this type of Bayesian optimization framework is implemented for DREAM and explored for current quench simulations for the JET plasma discharge #95135, previously investigated with DREAM simulations [4]. The proof-of-principle framework is able to find the optimum input parameters with uncertainties in both one and five dimensional optimization tasks explored in this work. The workflow is implemented using the Bayesian Optimization for Likelihood-Free Inference (BOLFI) method in the Engine for Likelihood-Free Inference (ELFI) Python software library [2, 5].
[1] M. Hoppe, O. Embreus, and T. Fülöp *Computer Physics Communications* **268** (2021) 109098.
[2] M.U. Gutman and J. Corander *Journal of Machine Learning Research* **17** (2016) 1-47.
[3] C.E. Rasmussen and C.K.I. Williams *Gaussian processes for machine learning*, MIT Press, 2006.
[4] B. Brandström *Spatio-temporal analysis of runaway electrons in a JET disruption with material injection*, Master’s thesis, Chalmers University of Technology, 2021.
[5] J. Lintusaari, et al. *Journal of Machine Learning Research* **19** (2018) 1-7.
**Acknowledgements:** *This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. The authors wish to acknowledge CSC – IT Center for Science, Finland, for computational resources.*