Abstract
This work suggests several methods of uncertainty treatment in multiscale modelling and describes their application to a system of coupled turbulent transport simulations of a tokamak plasma. We propose a method to quantify the usually aleatoric uncertainty of a system in a quasistationary state, estimating the mean values and their errors for quantities of interest, which is average heat fluxes in the case of turbulence simulations. The method defines the stationarity of the system and suggests a way to balance the computational cost of simulation and the accuracy of estimation. This allows, contrary to many approaches, to incorporate of aleatoric uncertainties in the analysis of the model and to have a quantifiable decision for simulation runtime. Furthermore, the paper describes methods for quantifying the epistemic uncertainty of a model and the results of such a procedure for turbulence simulations, identifying the model’s sensitivity to particular input parameters and sensitivity to uncertainties in total. Finally, we introduce a surrogate model approach based on Gaussian Process Regression and present a preliminary result of training and analysing the performance of such a model based on turbulence simulation data. Such an approach shows a potential to significantly decrease the computational cost of the uncertainty propagation for the given model, making it feasible on current HPC systems.
Supported by organisation “Munich School of Data Science”.
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References
EasySurrogate github. https://github.com/wedeling/EasySurrogate. Accessed 2 Mar 2023
Borgdorff, J., et al.: Distributed multiscale computing with MUSCLE 2, the multiscale coupling library and environment. J. Comput. Sci. 5(5), 719–731 (2014). https://doi.org/10.1016/j.jocs.2014.04.004
Brajard, J., et al.: Combining data assimilation and machine learning to infer unresolved scale parametrization. Phil. Trans. R. Soc. A: Math. Phys. Eng. Sci. 379(2194) (2021). https://doi.org/10.1098/rsta.2020.0086
Coster, D., et al.: The European transport solver. IEEE Trans. Plasma Sci. 38(9), 2085–2092 (2010). https://doi.org/10.1109/TPS.2010.2056707
Coster, D., et al.: Building a turbulence-transport workflow incorporating uncertainty quantification for predicting core profiles in a tokamak plasma. Nuclear Fusion (2021)
Edeling, W., et al.: The impact of uncertainty on predictions of the CovidSim epidemiological code. Nat. Comput. Sci. 1(2). https://doi.org/10.1038/s43588-021-00028-9
Falchetto, G., et al.: The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results. Nucl. Fusion 54(4), 043018 (2014). https://doi.org/10.1088/0029-5515/54/4/043018, 00005
Imbeaux, F., et al.: A generic data structure for integrated modelling of tokamak physics and subsystems. Comput. Phys. Commun. 181(6), 987–998 (2010). https://doi.org/10.1016/j.cpc.2010.02.001
Jancauskas, V., Lakhlili, J., Richardson, R., Wright, D.: EasyVVUQ: verification, validation and uncertainty quantification for HPC simulations (2021). https://github.com/UCL-CCS/EasyVVUQ
Leiter, K., Barnes, B., Becker, R., Knap, J.: Accelerated scale-bridging through adaptive surrogate model evaluation. J. Comput. Sci. 27, 91–106 (2018). https://doi.org/10.1016/j.jocs.2018.04.010
Luk, O., et al.: ComPat framework for multiscale simulations applied to fusion plasmas. Comput. Phys. Commun. 239, 126–133 (2019). https://doi.org/10.1016/j.cpc.2018.12.021
Lütjens, H., Bondeson, A., Sauter, O.: The CHEASE code for toroidal MHD equilibria. Comput. Phys. Commun. 97(3), 219–260 (1996)
Piontek, T., et al.: Development of science gateways using QCG—lessons learned from the deployment on large scale distributed and HPC infrastructures. J. Grid Comput. 14(4), 559–573 (2016). https://doi.org/10.1007/s10723-016-9384-9
Preuss, R., von Toussaint, U.: Global optimization employing Gaussian process-based Bayesian surrogates. Entropy 20 (2018). https://doi.org/10.3390/e20030201
Rasmussen, C.E., W.K.: Gaussian Processes for Machine Learning. The MIT Press (2006). https://doi.org/10.7551/mitpress/3206.001.0001
Scott, B.D.: Free-energy conservation in local gyrofluid models. Phys. Plasmas 12(10), 102307 (2005). https://doi.org/10.1063/1.2064968
Sobol, I.: On sensitivity estimation for nonlinear mathematical models. Math. Model. 2(1), 112–118 (1990)
Sullivan, T.: Introduction to Uncertainty Quantification. TAM, vol. 63. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23395-6
Vassaux, M., et al.: Ensembles are required to handle aleatoric and parametric uncertainty in molecular dynamics simulation. J. Chem. Theory Comput. 17(8) (2021). https://doi.org/10.1021/acs.jctc.1c00526
Veen, L.E., Hoekstra, A.G.: Easing multiscale model design and coupling with MUSCLE 3. In: Krzhizhanovskaya, V.V., et al. (eds.) ICCS 2020. LNCS, vol. 12142, pp. 425–438. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-50433-5_33
Acknowledgements
The authors of this paper would like to acknowledge the support of the Poznan Supercomputer and Networking Centre (PSNC) and Max-Planck Computational Data Facility (MPCDF). Research by Yehor Yudin is funded by the Helmholtz Association under the “Munich School for Data Science - MuDS”.
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Yudin, Y., Coster, D., von Toussaint, U., Jenko, F. (2023). Epistemic and Aleatoric Uncertainty Quantification and Surrogate Modelling in High-Performance Multiscale Plasma Physics Simulations. In: Mikyška, J., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2023. ICCS 2023. Lecture Notes in Computer Science, vol 10476. Springer, Cham. https://doi.org/10.1007/978-3-031-36027-5_45
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