As can be seen from Figs. 7 and 8 our results show interesting trends related with the temperature of the stars. In general, temperature is the dominating factor for the shape of and even the details in a spectral energy distribution. Overall, $T_{\rm eff}$ can be retrieved to very acceptable accuracy, even without additional UV information: the classification is better than 10% even for very faint stars (V=14 mag, no extinction included: through this section the V magnitude refers to end-of-mission quality data). Including UV fluxes improves the $T_{\rm eff}$ parameter results most noticeably for hot stars ( $T_{\rm eff}$ > 9000 K) and here especially for the fainter ones. For example, in case of no extinction, the error for DISPIs with V=14 mag in the $T_{\rm eff}$ range 12 000-20 000 K (H1 sample) drops from 5% to about 3% when the UV data are included. When extinction is included, the temperature error drops from 9% to about 4% for this temperature range at this magnitude. Though the information in the short wavelength range is already available in the DISPI, the higher sensitivity of the UV telescope obviously contributes essential information.

$\begin{figure} \par\includegraphics[width=15cm,clip]{H4080F8.eps} \end{figure}$

Figure 8: The same as in Fig. 7 but with extinction included. The left column shows the results for networks which were trained with UV data while the right column shows the classification results for tests without UV data.

Concerning $\log g$ we see from the figures that the classification performance can be improved when additional UV information is included. For example, in case of no extinction and for temperatures in the range 8000 K $\leq$ $T_{\rm eff}$ < 10 000 K (M₁) and visual magnitude V=14, the error in $\log g$ reduces from about 0.4 to 0.15 dex with additional UV information. At this magnitude but for temperatures in the range 6000 K $\leq$ $T_{\rm eff}$ < 8000 K (L₃), the error reduces considerably from about 0.85 dex to 0.15 dex. These results emphasize the benefit of UVtelescope data in the classification process. In general, the $\log g$ results are poorer for temperatures in the range 4000 K $\leq$ $T_{\rm eff}$ < 6000 K (L₂ sample) when compared to other ranges. This is understandable since in this temperature range hardly any atomic/molecular signatures sensitive to the density (and thus $\log g$ ) of the gases in a stellar atmosphere are present. In contrast, for the very low temperature ranges the numerous mostly molecular spectral features provide the information about the density of the atmospheric gases. For the higher temperatures the Balmer jump provides still gravity information.

Metallicity is the most difficult parameter to derive from DISPIs. This was to be expected: in data with such low spectral resolution all details of spectral line information, and thus of metal abundances, are lost. In Figs. 7 and 8 only the classification results for metallicities in the range -0.3 dex to 1.0 dex are shown. This is due to a lack of input data in the metallicity range from -2.5 dex to -0.3 dex (see above). Very low metallicities ([M/H] $\leq$ -2.5 dex) make only a very small imprint on a DISPI such that the classification almost fails completely at these resolutions, except for very bright, cool stars ( $T_{\rm eff}$ $\leq 4000$ K). The results for metallicities in the analysed metallicity range are reasonably good even for low magnitudes (better than about 0.3 dex for $V \leq 14$ mag, no extinction). When extinction is included, the metallicity performance declines considerably, except for the very cool objects ( $T_{\rm eff}$ < 4000 K, L₁ sample) the metallicity of which can be determined to better than 0.3 dex for all simulated magnitudes. For DISPIs in the temperature range 6000 K $\leq$ $T_{\rm eff}$ < 7000 K (L₃) we see that the error can be reduced from about 0.45 dex to 0.3 dex (no extinction) and from about 0.8 dex to 0.6 dex (with extinction) when the UV information is included.

Extinction is not easy to be retrieved solely from the shape of a DISPI, since its overall effect mimics, to some extent, that of temperature. However, as can be seen from the figures, the determination of extinction improves when the UV information is included. This was to be expected since the UV data gives the strength of the Balmer jump, giving $T_{\rm eff}$ information unblurred by extinction.

One may ask whether the accuracy of the parameters derived would be better when working with the single orders of the DIVA dispersed image. We have tested this for a limited number of parameter combinations. We generally found that for brighter objects ( $V \leq 13$ mag) the accuracy is improved when using the single orders and then only by a small amount (in the range 30 to 80 effective pixels). This might be surprising at first but it is understandable since for fainter objects, using the signal in a single order, deteriorates the S/N, so we find a poorer result from the parameter extraction routine. Apart from these results, to obtain the separate order's signals would require a deconconvolution of the DISPI which in itself leads to increased uncertainty in the intensities. Moreover, a deconvolution requires knowledge of the nature of the objects so there is no guarantee that this process will yield unique results. Since DIVA will not have separate order images we have not pursued this aspect further.

Several neural network approaches to stellar parametrization have been reported in astronomy. A comparison with those would have to address at least two aspects, such as nature of the type of network and characteristics of the data used. The networks may indeed be very different in structure such as learning and regularization technique and especially topology (compare e.g. Weaver & Torres-Dodgen 1995; Snider et al. 2001 and this work). But because in all these cases the data were of very different nature (e.g. different resolutions and number of input flux bins), a general comparison of the results is not really possible. A few remarks can be made nevertheless.

Projects to obtain MK classifications normally use data in the wavelength range from 3800 to 5200 Å with high spectral resolution of about 2 to 3 Å (see e.g. Bailer-Jones et al. 1998). Weaver & Torres-Dodgen (1995) and Weaver & Torres-Dodgen (1997) classified stars in terms of MK classes in the visual to near-infrared wavelength range 5800-8900 Å with a resolution of 15 Å. However, even the resolution of these spectra is still much better (by a factor of approx. three) than the "best" one of DISPIs which is about 40 Å in the low efficiency third order. We would expect such resolutions to give better precision for spectral type or $T_{\rm eff}$ as well as for line sensitive parameters ( $\log g$ and [M/H]) than with DISPIs on account of the higher resolution. Snider et al. (2001) recently classified spectra having 1 to 2 Å resolution. They determined $T_{\rm eff}$ , $\log g$ and [M/H] of low metallicity stars to an accuracy of about 150 K in $T_{\rm eff}$ in the range 4250 K < $T_{\rm eff}$ < 6500 K, 0.30 dex in $\log g$ over the range $1.0 \leq\$ $\log g$ $\ \leq 5.0$ dex and 0.20 dex in [M/H] for $-4 \leq\$ [M/H] $\ \leq 0.3$ dex. From our results, we find for this temperature range (L₂ and L₃ sample) a classification precision in $T_{\rm eff}$ of better than 5% for $V \leq 14$ mag (no extinction) without UV information and about 2% when UV data are included. Only for brighter stars ( $V \leq 13$ mag) do we find that $\log g$ can be determined from DISPIs to better than 0.3 dex for temperatures in the range 4000 K $\leq$ $T_{\rm eff}$ < 6000 K but only when UV data are included. Concerning metallicity, our results are comparable (better than 0.2 dex for visual magnitudes $V \leq\ 12$ mag, no extinction, UV data included). Clearly, this is because we have only used metallicities in the range from -0.3 dex to +1 dex (see above).

A comparison with the neural network approach using synthetic data for a test of possible GAIA photometric systems (Bailer-Jones 2000) may be of relevance. Bailer-Jones also used input data with various moderate resolutions, some of them similar to those of the spectral orders in DISPIs. The effects of the quantum efficiency (QE) of the detectors was not included, so that in his tests the information provided in the vicinity of (and shortward of) the Balmer jump could be utilized in full. After shifting our results to the fainter magnitudes reachable with GAIAs larger telescope, while considering the other differences between Bailer-Jones' and our investigation as well as the differences between the DIVA and GAIA optics and data format, one must conclude that these ANN analyses work to similar satisfaction.

Little work has been done so far concerning the automated determination of interstellar extinction. Weaver & Torres-Dodgen (1995) tested the effect of extinction and found that E(B-V) could be determined from spectra of A type stars with an accuracy of 0.05 mag in the range of E(B-V) of 0-1.5 mag. Gulati et al. (1997) used IUE low-dispersion spectra (wavelength range 1153-3201 Å, spectral resolution 6 Å) from O and B stars. Applying reddening to their spectra in the E(B-V) range of 0.05-0.95 mag in steps of 0.05 mag, they were able to retrieve extinction with high accuracy to about 0.08 mag, clearly because of the presence of the 2200 Å bump in the input data. From Fig. 8 we see that extinction can be determined from DISPIs to better than 0.08 mag for visual magnitudes $V \leq 14$ mag for all temperatures in case that UV data are included.

Concerning the DIVA satellite, Elsner et al. (1999) found interesting results with Minimum Distance Methods. However, the optical concept of DIVA has changed considerably since then. Thus, also here a comparison of the quality may lead to a skewed judgement and we therefore refrain from going into detail.

A final remark deals with the effect of selecting our training sample randomly from the database. A random selection may accidentally lead to larger regions of parameter space without training data. Since our object ("application") sample is the complement of the training set, objects falling in those gaps clearly are classified worse than objects near trained points. Malyuto (2002) demonstrated such effects when using Minimum Distance Methods. The average errors in our results are influenced by such effects, but this was not investigated.

In considering the accuracies obtained with our ANN approach we have to note that real stellar spectra show a much more complex behaviour than synthetic ones. For example, even the more realistic approach of non-LTE models (Hauschildt et al. 1999) cannot properly describe the true behaviour of elements in a stellar atmosphere (see e.g. Gray 1992, Chap. 13). Moreover, good colour calibrations in accord with observed data are still difficult to obtain, as described e.g. in Westera et al. (2002). It is difficult to estimate how to properly weigh such intrinsic inconsistencies with respect to the final performance of the DIVA satellite. The effect of such cosmic scatter probably is that the final performance of DIVA might be less accurate than our results from these ideal synthetic spectra, or, that the accuracy curves of Figs. 7 and 8 are to be shifted somewhat to brighter magnitudes.

We argued that additional UV data can improve the parameter results considerably in the classification process. The spectral library of our present simulations does not include, however, changes in, e.g., alpha-process elements which can show up in changes also in the range of DIVA's UV channels (e.g. the CN violet system in the range from 385 to 422 nm).

The conclusions of the discussion are
1) The ANN method is well suited to obtain astrophysical parameters from DIVA DISPIs.
2) The accuracy obtained is related with the strength of the signal of each parameter as present in a DISPI: $T_{\rm eff}$ is best, followed by $\log g$ , and then E(B-V) and [M/H].
3) The accuracy is clearly related with temperature: toward higher temperature the signal of both $\log g$ and [M/H] decreases considerably.
4) Our results were obtained with synthetic spectra. Real stars will not all behave like text book objects and the classification coming from real data will necessarily be less good, albeit always to an unknown amount per star.
5) The classification quality is absolutely adequate to be able to select objects of desired characteristics from the final DIVA database to do statistical analyses and/or for efficient post mission type-related investigations.

Note added in proofs: The German Aerospace Center (DLR) informed the DIVA project mid Feb. 2003, that the DIVA mission had to be cancelled due to financial problems. Nonetheless, many of the ideas and techniques presented within this article are of relevance to other future (spectro)photometric projects, such as the GAIA astrometry mission (Perryman et al. 2001) of the European Space Agency (ESA).

7 Discussion and conclusions