7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Plausible model creation by means of data assimilation

Masayuki Yokoyama, Yuya Morishita1 and Sadayoshi Murakami1
National Institute for Fusion Science (NIFS) Rokkasho research Center,
National Institutes of Natural Sciences (NINS)SOKENDAI,
1
Department of Nuclear Engineering, Kyoto University,e-mail (speaker): yokoyama@nifs.ac.jp
Data assimilation technique has been successfully
implemented into the fusion research [1,2], andfurthermore, it has been advancing toward real-time
control of fusion plasmas, which is the leading progresseven in the field of data assimilation research (such asthe weather forecast and the oceanology) [3].

given model (Ci to be radially constant) and validate
model against measured data through data assimilation.
It is noted that Ci=1 in the horizontal axis corresponds tothe “radially-constant Ci model”. Figure 2 indicates acertain trend of Ci, which provides valuable hints forwhat was missing in the previous model.

During the data assimilation process, given
physics-based or empirical models can be optimized by
employing the observation data. Thus, for example, inthe thermal transport problem of fusion plasmas, thevalidated model (so as to fit to or to reproduce theobservation data) can be obtained. In this presentation,plausible model creation by means of data assimilation isdescribed, taking the thermal transport coefficient offusion plasmas as an example.

Thus, it is expected that a plausible physics model (orphysics interpretation beyond the originally assumed
model, GyroBohm in this case) could be created byexpressing this recognized trend of Ci with physics
variables. An immediate example for doing this is toconduct multivariate regression analysis for Ci. This trial
has been conducted, and the resultant“statistically-reasonable” expression for Ci was obtainedas,

In the previous research in the Large Helical Device(LHD) [4,5], ion thermal transport coefficient wasmodeled by comparatively referring measured andsimulated (by integrated transport analysis by TASK3D[5]) ion temperature profiles (total of only 8 cases: 1
timing each from 8 NBI-heated discharges) to deduce
plausible modification to Gyro-Bohm model. The
obtained ion thermal transport coefficient is described asfollows.

Here, Ci is the radially-constant value, and all othervariables follow the conventional notation. It is notedthat the deduced model is only valid to limited number ofcases (8 time slices, in this case). When this model isprovided to TASK3D and the time evolution simulationfor other discharge (but with similar NBI-heateddischarge) is performed, it hardly reproduces thetime-series data of measured ion temperature. This fact
clearly shows that “time slice-based” model creation is
not enough to provide reasonable prediction to overallbehaviour of fusion plasmas.
On the other hand, data assimilation of NBI discharges(12) with even Ci to be the state variable (allowingvariations even radially during the model optimization
process, by maintain compatibility with all other statevariables [1]) has accumulated radial profiles of Ci forall data assimilation cycles in these 12 discharges. Thisaccumulated information on Ci displays the gap between

based on the application of Akaike’s Information
Criterion (AIC) [6] (more precisely, AICc with acorrection for small sample sizes) [7] for selectingstatistically important variables among a priori prepared
physics variables.
As above described, a way of deducing physics
models in fusion plasmas could be proposed (not onlyfor thermal transport issues) by means of data
assimilation.
References[1] Y. Morishita et al., Nucl. Fusion 60 (2020) 056001.
[2] Y. Morishita et al.,, Computational Physics
Communications 274 (2022) 108287.
[3] Y. Morishita et al., J. Computational Science 72(2023) 102079.
[4] A. Wakasa et al., , 39th EPS (2012) P2.028.
[5] S. Murakami et al., Plasma Phys. Control. Fusion 57(2015) 054009.
[6] Akaike H, "Information theory and an extension of
the maximum likelihood principle", 1973 Proceedings ofthe 2nd International Symposium on Information Theory,Petrov, B. N., and Caski, F. (eds.), Akadimiai Kiado,
Budapest 267.
[7] Sugiura N, Communications in Statistics – 1978
Theory and Methods 7 13
Acknowledgements will be described in the presentation.