Phenomenological dynamics of coronal loops using a neural network approach

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Adv. SpuceRes. Vol. 2.5, No. 9, pp.1917-1921.2000 Q 2CNMCOSPAR. Published by Eisevier Science Ltd. All rights resewed Printed in Great Britain 0273- 1177/00 $20.00 + O.OfI PII: SO273-1177(99)00624-9

PHENOMENOLOGICAL DYNAMICS OF CORONAL USING A NEURAL NETWORK APPROACH

LOOPS

R. R. Rosal, H. S. Sawant2, J. R. Cecatto2, C. Rodrigues Neto’, V.C.A. Lopesl, K.R. Subramanian2, F.C.R. Fernandes”, J. H. Saito3, C. E. Morona, M. L. Mucheroni3, N. Furuya3, and N. Mascarenhas3 ‘Lab. for Computing and Applied Mathematics (LAC) - INPE, S6o Jose’ dos Campos, SP, Brazil 2Astrophysics Division (DAS) - INPE, Sa”o Jose’ dos Campos, SP, Brazil 3 Computing Depa rtment - Universidade Federal de S&o Carlos, S6o Carlos, SP, Brazil

ABSTRACT The objective of this study is to simulate the X-ray SD-coronal dynamics using an artificial neural network multilayer backpropagation algorithm with inputs of Energy Fragmentation Patterns obtained from Yohkoh images in soft and hard X-rays. Details of a single loop structure have been investigated for initial analysis. The images are spatio-temporal series showing the loop-top in Soft X-ray (SXR) and foot points in Hard X-ray (HXR). Using a square electron density gradient model, we have characterized the spatio-temporal loop dynamics concerning its twister-relaxation regime. The performance of this trained network model has been tested with classical image statistics applied to the Yohkoh data. In this paper we show preliminary results indicating that this technique can be useful for coronal dynamics analysis. 0 2000 COSPAR. Publishedby Elsevier Science Ltd. INTRODUCTION Yohkoh X-ray images of the solar atmosphere have revealed the existence of structures with magnetic field configuration varying from regular (e.g., single set of loops) to complex patterns (e.g., filament eruptions). However, there is a lack of studies about the dynamics of such structures, mainly the ones involving nonlinearities and energy fragmentation. The first limitation for these studies is the simplicity of the models in terms of spatio-temporal non-linearities and randomness. Recently, Rosa et al. (1997a) have reported the characterization of localized turbulence as the physical processe driving the dynamics of soft X-ray eruptive phenomena observed by Yohkoh. Also they reported (Rosa et al., 1997b) the fragmentation analysis of regular structures, suggesting a dynamical empirical scenario for coronal active regions as a candidate to generate geomagnetic storms. However, these studies have been made for 2D-images without information about the 3D-source configuration. This is a limitation about the internal characteristics of the source. In this paper we report a preliminar report on the Brazilian Coronal Tomography Project (BCTP) where we proposed an Artificial Intelligent System (AIS) to learn about the 2D-dynamics of Yohkoh X-ray structures and an extension of that to reconstruct a tomographic image of the internal distribution of the source energy. In Section 2 we introduce the AI system we have been developing. Preliminary results are in Section 3. In the last section we discuss the results and applications of the technique.

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1918

THE

R. R. Rosa et al.

NEURAL

NETWORK

LOOP

SIMULATOR

The neural network (NN) is arranged in layers of processing elements where each one gives as output the transformed weighted sum input. This system is based on the multi-layer feed-forward error backpropagation (FFEB) paradigm (Hertz et al., 1991). Our system is a multi-channel NN as shown in Figure 1. Each channel is a net of four layers: ke, kr , IQ and ka. The input is denoted by ko, hidden layers are Ici and k-2 and the output layer is k3. In the feed-forward phase, the input is propagated forward through the net to the output. The net output, for an input pattern p, depends on the activation function g. This is a sigmoid which should be a differentiable function able to saturate at both extremes. If there exists a relation between the input, 1i, and the output,Oj, the NN learns by adjusting the weights until an optimum set of weights is obtained that minimizes the network error. This is a convergence driving by the network error, E, defined as E = f 2

k(T;

- q)“,

(1)

p=l j=l

where TT is the target

value, and the output

The standard

rule is an iterative

learning

function

process which updates

Aw(t + 1) = -@g where p and (Yare the learning

rate and the momentum

the weights according

to

+ crAw(t),

term, respectively.

We used the neural network routines from MATLAB to construct the 3 Channel-Loop-Simulator similar to the Ichikawa-simulator (Ichikawa, 1993): a FFEB model which is applied as a non-linear, multi-variable, least squares algorithm. The input is a matrix m x m with m 5 256 and its degree of asymmetric energy fragmentation. This is written as the input pattern p. This pattern is composed by the Ii inputs generated by the empirical models obtained from the 2D-Kuznetsov-Hood scenario (Kuznetsov and Hood, 1997). These equations are for the non-equilibrium twisted magnetic flux tubes emerging into the solar corona. The channel S is for the simulation of the top of the loop emiting soft X-ray. The target pattern Tj for this channel is composed by the emission measurement unit from the pixels of a SXR Yohlcoh image. The channel H is for the simulation of the footpoints of the loop emiting hard X-ray. The target pattern Tj for this channel is composed by the emission measurement unit from the pixels of a HXR Yohkoh image. The channel L is for the simulation of the profile of the loop emiting hard and soft X-ray. The target pattern Tj for this channel is composed partially by the emission measurement unit Erom the pixels of a SXR Yohlcoh image of a loop observed at the solar limb. With the set of these three images, we will be able to construct further a 3D-tomographic image of the coronal structure (e.g. a single loop). Solar X-ray tomography represents a mathematical deconvolution problem, where a 3D-density distribution is deconvolved from many line-of-sight integrals of X-ray emissivity. As pointed out by Aschwanden and Bastian (1995), tomography of the solar corona via freefree emission seems to be the most promising in soft X-ray wavelengths, where the emission is always optically thin and is detectable almost from the Solar tomographic research is being developed jointly with the Compvting Department whole corona. of Uniuersidade Federal de Silo Carlos (UFSCar) that is responsible for the construction of a dedicated parallel machine to make the coronal tomography (Moron et al., 1997).

Neural Network Loop Simulator k=2 k=l _______-_____-w-w-

I

1919 k=3 ------I

cHINMU

,

YD-S

YD-L

YDH

Figure 1 - The Neural NetworkLoop Simulator (NNLS).

PRELIMINARY

RESULTS

The performanceof the trained network has been tested for ChannelsS and H of the NNL-simulator.Soft and Hard X-ray images from the top and from the footpoints of the loop, respectively,have been obtained. The data set used for both channels is composed by 7 images from the Yohkoh data set from ISAS. The empiricaldynamics of the model loop is given by the time-evolutionof the Asymmetric Fragmentation parameterintroduced by Rosa et al. (1997a), applied on the ZD-matricesobtained from a phenomenological 2D-Kusnetsov-Hood-likescenario. The loop patternsare set statiscallyfrom random matrices (Rosa et al., 1999). In Figure 2 (a,b,c), we show the simulated loop dynamics obtained from channel S. Its twisted-relaxed dynamics is charaterizedby the variationof asymmetricenergy fragmentationas shown by the solid line in Figure 4. In Figure 3 (a,b,c), we show the simulatedioop dynamics obtained from channel H. Its twistedrelaxed dynamics is charaterised by the variation of asymmetric energy fragmentation as shown by the dotted line in Figure 4.

R. R. Rosa er al.

1920

(a) trme-step 1

(b) time-step 2

(c) trme-step 3

Fig. 2 - The simulated loop top at time-step 1 (a), 2 (b) and 3 (c).

(b) time-step 2

(a) time-step 1

(c) time-step 3

Fig. 3 - The simulated loop foopoints at time-step 1 (a), 2 (b) and 3 (c).

0.75

-

g .a m ti 5) d r&

4

0.50

-

0.25

-

AFS

2

3 $

3

4

I

I

1

2

3

time-step Fig. 4 - the time-evolution of fragmentation parameter during the simulated loop-top dynamics (solid line), and the time-evolution of fragmentation parameter during the simulated loop-footpoint dynamics (dotted line).

CONCLUDING

REMARKS

The behaviour of both simulations S and H is consistent with real loop dynamics phenomenology. The variation of fragmentation parameter for case S is larger than that of the case H. Thii means that the energy configuration of the loop top has more degrees of freedom than that of the footpoints where the magnetic field is more intense and the plasma is more confined. This result suggests the NNL-Simulator can also be used to characterize the dynamics of more complex regions. For example, the phenomenological analysis of localized turbulence from complex soft-X ray structures has been reported by Rosa et al. (1997a). This

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Neural Network Loop Simulator

investigation could be used to develope an empirical model whose pattern can be a target in the NNLoop Simulator. This model of the simple loop will be applicable to a system of loops known as eruptive structures.

At Instituto National de Pesquisas Espaciaas (INPE), efforts have been made to develope decimeter Radio Heliograph, so that some of the theoretical results can be also compared to actual radio images obtained by this radioheilograph. Analysis of radio observations will be important to improve prediction criteria of geomagentic disturbances and to study solar terrestrial relations. It will be helpful in future solar maxima to avoid the effects of radio blackout caused by flares. In short, the characterization of self-organization regimes of complex coronal structures, in 2 and 3D, is the main goal of the scientific research that will be developed in the Latin-American Space Weather Forecasting Program (LASWFP) scheduled to start in 1999 (Rosa et al. 1998). ACKNOWLEDGEMENTS We would like to thank Alexandre Guido and Renata S. Paula for computer support and staff of Computing Department of Universidade Federal de Sao Carlos, and the Yohkoh team for the hard and soft X-ray data specially to Dr. Masuda from STELAB (Nagoya University). We are also grateful to the referees for valuable suggestions. RRR is grateful to the brazilian agency FAPESP under PROC 97/13374-l. REFERENCES Aschwanden, M.; T.S. Bastian, 426, 434 (1995).

VLA stereoscopy of solar active regions, Astrophysical Journal,

Hertz, J., A. Krogh; R.G. Palmer, Introduction to the theory of neural computation, Lectures Notes, Vol. 1, Addison-Wesley (1991).

Santa Fe Institute,

Ichikawa, H., Layered Neural Networks, p. 108, Kyoritu Pub., Tokyo (1993). Kuznetsov, K.; D. Hood, Non-equilibrium of magnetic flux tubes emerging into the solar corona, Solar Phys., 172, 323 (1997). Moron, C.; Saito, J.H.; Abib, S.; Mucheroni, M.; Furuya, N.; Battaiola, A.; Sawant, H.S.; Rosa, R.R.; Cecatto, J.R.; Alonso, E.B., Parallel architecture using DSPs, in Proc. of IX Simpdsio de Arquitetura de Comput. - PAD, SBAC ed. pp. 605-608 (1997). Rosa, R.R.; H.S. Sawant, H.S.; J.A. Valdivia; A.S. Sharma, Dissipative structure and weak turbulence in the solar corona, Adv. Space Res., 20, 2303 (1997a). Rosa, R.R.; H.S. Sawant; J.A. Valdivia; A.S. Sharma; N. Srivastava; W.D. Gonzalez, Characterization of spatio-temporal turbulence in the solar corona: an application for geomagnetic storm forecasting, in Proc. of V Int. Sch. Symp. for Space Simulations, Kyoto, RASC ed. pp. 282-286 (1997b). Rosa, R.R.; H.S. Sawant; F.M. Ramos; A.S. Sharma; J.A. Valdivia, Space weather phenomelogy and forecasting by using pattern recognition operators, in Fifth Latin-American Conference on Space Geophysics, San Jo&, C. Rica, 3-7 November 1998, V-COLAGE Abstracts p. 138 (1998). Rosa, R.R.; N. Mascarenhas; C. Moron; J.H. Saito, Statistical sampling analysis of X-ray solar images, In submission to Intern. Journal of Modern Physics C (1999).