Inthis paper we have for the first time applied the new Stokes inversion approach of using artificial neural networks to measured Stokes data of a solar pore. We have demonstrated that this method is capable to produce the same

results as other conventional methods, but at a much faster speed

Balthasar, H.

Carroll, T.A.

Collados, M.

Muglach, K.

English

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IL NUOVO CIMENTO Vol. 25 C, N. 5-6 Settembre-Dicembre 2002Application of artificial neural networks to solar infrared Stokesspectra(∗)T. A. Carroll(1), K. Muglach(1), H. Balthasar(1) and M. Collados(2)(1) Astrophysikalisches Institut Potsdam - Germany(2) Instituto de Astrofisica de Canarias - Tenerife, Spain(ricevuto il 10 Giugno 2002; approvato il 7 Agosto 2002)Summary. — In this paper we have for the first time applied the new Stokesinversion approach of using artificial neural networks to measured Stokes data of asolar pore. We have demonstrated that this method is capable to produce the sameresults as other conventional methods, but at a much faster speed.PACS 95.75.Pq – Mathematical procedures and computer techniques.PACS 95.75.Hi – Polarimetry.PACS 95.75.Wx – Time series analysis, time variability.PACS 96.60.Qc – Sunspots, faculae, plages.PACS 95.85.Jq – Near infrared (0.75–3 µm).PACS 01.30.Cc – Conference proceedings.1. – IntroductionIn September 1999 a joint observing campaign was carried out (JOP097, see http://sohowww.nascom.nasa.gov/soc/JOPs/jop097.txt). The general aim of this campaignwas to study the oscillatory behaviour of active regions with a variety of instrumentsand observing modes. In this contribution we apply artificial neural networks to invertmeasured Stokes spectra and we compare this new method with other, more traditionalways to retrieve physical quantities from the Stokes spectra.2. – ObservationsNear infrared observations were taken with the Tenerife Infrared Polarimeter (TIP [1])at the VTT. The complete Stokes vector was measured for about 90 min with the Fe Ilines at 15648 A˚ and 15652 A˚ at a cadence of 15.5 s. We observed AR 8693 (located(∗) Paper presented at the International Meeting on THEMIS and the New Frontiers of SolarAtmosphere Dynamics, Rome, Italy, March 19-21, 2001.c© Societa` Italiana di Fisica 581582 T. A. CARROLL ETC.Fig. 1. – Photospheric image of AR 8693 taken with TRACE. The diagonal line indicates theposition of the VTT slit.at 13 N, 20 E) which also included a large pore, which we selected for this analysis.Figure 1 shows a photospheric white-light image of the active region taken with TRACE.Two times four rows of spectra in the central part of the pore are averaged and theobserved parameters are calculated separately for these two positions. Details of thedata reduction and analysis as well as results of this oscillation study are publishedin [2].In this paper we will concentrate on two particular parameters, namely velocity v andmagnetic-field strength B which we derive with three different methods from the samedata set. Method 1 (described in [2]) calculates v and B directly from the observed Stokesparameters: the magnetic-field strength is obtained from a comparison of the observedStokes V profiles with the calculated ones. This method is sensitive to the splitting ofthe V profile. Velocities are derived from the mean values of the positions of the twoStokes V extrema.In method 2 we used the SIR inversion code developed by [3] to get v and B fromStokes I and V profiles of both lines with a high weight on Stokes V . SIR yields astratification for temperature, electron pressure, magnetic-field strength, inclination andazimuth, Doppler velocity and microturbulence depending on an initial model atmosphereand on demands. From the results we extracted magnetic-field strength and Dopplervelocity at log τ = 0 for this presentation.Finally, we applied artificial neural networks for a direct inversion of the desiredquantities from the observed Stokes spectra.3. – The neural-network approachWe have used a Multi-Layer-Perceptron (MLP) to find a direct approximation ofthe non-linear inverse relation between the Stokes profiles and the atmospheric parame-ters [4]. A detailed description of this method is given in [5]. Multi-Layer-Perceptrons—APPLICATION OF ARTIFICIAL NEURAL NETWORKS ETC. 583Fig. 2. – Schematic illustration of the inversion process. The discrete Stokes V profiles (left)are preprocessed by a linear transformation and then presented to the MLP which represents anon-linear approximation for the inverse problem. In a final postprocess the calculated valuesare rescaled.as one particular type of artificial neural networks—are very general statistical tools forapproximating multivariate non-linear functions. Since we have a good knowledge aboutthe forward process of the polarized radiative transfer—at least under LTE conditions—we are able to train an MLP on a set of Stokes profiles and the underlying atmosphericparameters.The training process consists of an optimization of the adaptive parameters of theMLP. In this optimization process the network tries to approximate the functional map-ping which is represented by the input-output relation of the training set. Once a goodapproximation to the inverse problem is found, the MLP is able to retrieve reliable es-timates of the physical parameters from the observed Stokes spectra with exceptionalspeed. Figure 2 shows the inversion process in a schematic way.4. – Modelling the solar pore and training of the neural networkFor the inversion of Stokes profiles of the observed Fe I line at 15648.5 A˚ the MLPis trained on the basis of a modified semi-empirical pore atmosphere from [6]. We havecalculated a training set of 5000 synthetic Stokes profiles and another 3000 profiles asa validation set with the DIAMAG synthesis code (i.e. forward model) from [7] whichimplements a numerical integration of the radiative transfer equation by means of thediagonal lambda iteration method [8]. In order to achieve an appropriate representa-tion of the inverse mapping (Stokes profiles to atmospheric parameters), we take intoaccount the variation of six atmospheric parameters. The parameters for the calculationof the synthetic profiles are determined by a random generator. The intervals for theatmospheric parameters covering a range of 1000–3000 G for the magnetic-field strength,0–70◦ for the inclination, 0–120◦ for the azimuth, −1000– +1000 m s−1 for the line ofsight velocity, 0–1500 m s−1 for the microturbulence and 0–1000 m s−1 for the macro-turbulence.Since we are mainly interested in the retrieval of v and B, we decided to make onlyuse of the Stokes V profile as an input to the MLP. The discrete Stokes V profiles arecalculated in a wavelength range of +40 pm to −40 pm around the laboratory line centerwith a sample of 1 pm.The training data set is then used to train different network architectures (with dif-584 T. A. CARROLL ETC.Fig. 3. – Time sequence of magnetic field B (left) and velocities v (right) for two positions inthe pore (top row), below are the respective power spectra. The solid line results from method1 (Stokes V splitting), the dashed line from method two (inversion with SIR) and the dottedline from the MLP. The horizontal line represents the 98% significance level according to [9].The sequences of the two locations in the pore have a constant offset for clarity in the top paneland are shown seperately in the middle and bottom panel.ferent numbers of hidden layers and elements in those layers). After extensive statisticaltests on an independent test set we determined the network which performed best underthese tests for the following analysis of the oscillating behaviour of the observed pore.APPLICATION OF ARTIFICIAL NEURAL NETWORKS ETC. 5855. – Comparison of v and BFigure 3 (top, left) shows the time sequence of the magnetic-field strength B for the2 locations of the pore and the same for the velocity v (top, right). The sequences ofthe two locations in the pore have a constant offset for clarity in these plots. In themiddle and bottom panels the respective power spectra of v and B for each position inthe pore are shown. All three methods give very similar results, except SIR producinghigher power peaks in one case. Slight differences between the three methods might beexplained by the fact that we had to clip the short wavelength wing of the 15648 A˚ lineto be able to observe the other line simultaneously.Finally, we want to compare the computing times of the three methods. Each timesequence consists of 370 Stokes profiles from which v and B are determined. With SIR(method 2) it took about 2–3 days on a HP workstation. Calculation from Stokes Vsplitting (method 1) took about 2 h, and the MLP (method 3) took about 2 s for theinversion.∗ ∗ ∗We would like to thank P. Su¨tterlin for providing the pore model atmosphere.We would also like to thank our colleagues from the IAC for providing the SIR-code,especially L. Bellot Rubio for his help getting started with it. This research is part ofthe TMR-ESMN (European Solar Magnetometry Network) supported by the EuropeanCommission. The VTT on Tenerife is operated by the Kiepenheuer-Institut fu¨r Sonnen-physik (Germany) at the Spanish Observatorio del Teide of the Instituto de Astrof´ısicade Canarias.REFERENCES[1] Martinez Pillet V., Collados M., Sanchez Almeida J. et al., in High ResolutionSolar Physics: Theory, Observation and Techniques, edited by T. R. Rimmele, K. S.Balasubramaniam and R. Radick R., ASP Conf. Series, 183 (1999) 264.[2] Balthasar H., Collados M and Muglach K., AN, 321 (2000) 121.[3] Ruiz Cobo B. and del Toro Iniesta J. C., Astrophys. J., 398 (1999) 375.[4] Carroll T. A., Balthasar H., Muglach K. and Nickelt I., in Advanced SolarPolarimetry - Theory, Observation, and Instrumentation, edited by M. Sigwarth, ASPConf. Series, 236 (2001) 511.[5] Carroll T. A. and Staude J., Astron. Astrophys., 378 (2001) 316.[6] Su¨tterlin P., Astron. Astrophys., 333 (1998) 305.[7] Grossmann-Doerth U., Astron. Astrophys., 285 (1994) 1012.[8] Rees D. E., Murphy G. A. and Durrant C. J., Astrophys. J., 339 (1989) 1093.[9] Groth E. J., Astrophys. J. Suppl., 29 (1975) 285.

Application of artificial neural networks to solar infrared Stokes spectra

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Application of artificial neural networks to solar infrared Stokes spectra

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