1. Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz michael@damir.iem.csic.es Sun M51 Rosette CNSFR

2. Fundamental  Functional parameters Abundances AI - A new opportunity n-D Calibrations Ideas for the future De-projection Theory Physics & knowledge Emission Line Fluxes (I) Imaging Photoionisation Modelling & Simulation Empirical Relations & Calibrations Abundance indicators S23 O23 all fundamental parameters eta Softness parameter Abundance indicator S23 Z Metallicity Effective Temperature Ionisation parameter T* U Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

3. The IDEAL Indicator xn? Abundances AI - A new opportunity n-D Calibrations Ideas for the future Would be MONOTONIC with respect to metallicity Z Would be observationally detectable up to high Z Would have low average dispersion (least-square error) Would span a W I D E range of Zwhen empirically-calibrated using REAL galaxy data & IF ALL THAT WENT PERFECTLY… It would also be independent of chemical evolution and have an understandable behaviour with Z ? Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

4. Observational Limits at high Z Abundances AI - A new opportunity n-D Calibrations Ideas for the future Z=12+log(O/H)=8.66±0.05 Asplund et al 2004 Commonly used auroral-to-nebular emission line ratios… Bresolin 2006 8m telescope observing limit Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

5. Indicators in HII-like regions Abundances AI - A new opportunity n-D Calibrations Ideas for the future Galactic HII-Regions Extra-Galactic HII-Regions HII Galaxies CNSFRs? Perez-Montero 2002 Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

6. AI: An opportunity Abundances AI - A new opportunity n-D Calibrations Ideas for the future Scale-invariant And Genetic Algorithm Network(SAGAN) Architecture Weights Node Functions Dimensional Analysis Taylor & Diaz 2006 Net DNA Ecoding Multi-Layer Perceptron + Genetic Operators Mutation Cross-over + Back-Propagation + Pruning Algorithm UNIVERSAL FUNCTION APPROXIMATOR Taylor 2005 103 ERROR REDUCTION Taylor 2005 EQUATIONS Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

7. A new strategy Abundances AI - A new opportunity n-D Calibrations Ideas for the future LINE RATIOS 1 Emission line fluxes 4 5 6 2 3 GA (Genetic Algorithm) CALIBRATIONS About the sample Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

8. How it Works: e.g. Newton’s Law Abundances AI - A new opportunity n-D Calibrations Ideas for the future IDEAL SOLUTION m h3 1 1 a h3 h2 F e h3 PRUNED NODES inputs outputs Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

9. Newton’s Law: F=ma (EXACT) Abundances AI - A new opportunity n-D Calibrations Ideas for the future G=2 G=5 G=8 G=38 Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

10. Newton’s Law: F=ma (10% Errors) Abundances AI - A new opportunity n-D Calibrations Ideas for the future G=38 10% Errors G=780 G=995 G=161 Error Generation Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

11. HII-like regions: HIIGs, GHIIRs & EGHIIRs Abundances AI - A new opportunity n-D Calibrations Ideas for the future log(S23) elog(S23) SAGAN h3 h2 eZ Z e h3 e-space Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

12. Training & Evaluation Data Abundances AI - A new opportunity n-D Calibrations Ideas for the future Exponential Space Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

13. SAGAN Evolution (2 days on a dual 3Ghz PC) Abundances AI - A new opportunity n-D Calibrations Ideas for the future Taylor & Diaz, 2007, PASP, 374, 104 Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

14. Evolution of the calibration: Z=f(S23) Abundances AI - A new opportunity n-D Calibrations Ideas for the future Dispersion=0.183 dex Dispersion=0.22 dex Dispersion=0.181 dex Dispersion=0.16 dex Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

15. Fitting & n-D Calibrations Abundances AI - A new opportunity n-D Calibrations Ideas for the future e.g. Dimensionless Line Ratios Needs a big and homogeneous data-set Can potentially reduce subjectivity Can potentially identify new indicators Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

16. A sample for n-D studies Abundances AI - A new opportunity n-D Calibrations Ideas for the future Izotov et al 2006  144 objects (another 163 from other sources) using Pilyugin, Thuan and Vilchez, 2006 Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

17. Data classification with the BPT plot Abundances AI - A new opportunity n-D Calibrations Ideas for the future Kniazev et al 2004 This work Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

18. Metallicity and O23 Abundances AI - A new opportunity n-D Calibrations Ideas for the future Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

19. Metallicity and S23 Abundances AI - A new opportunity n-D Calibrations Ideas for the future ? Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

20. The role of S (S+, S2+, S, ICF) Abundances AI - A new opportunity n-D Calibrations Ideas for the future ! ? What do these curves depend on? Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

21. Trends of U and η with S23 Abundances AI - A new opportunity n-D Calibrations Ideas for the future U(o) U(o) v U(s) η T* or age? ZAMS Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

22. Data in the η-U-S23 space Abundances AI - A new opportunity n-D Calibrations Ideas for the future Clustering objects with Z Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

23. Fitting with a plane Abundances AI - A new opportunity n-D Calibrations Ideas for the future Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

24. Fitting with a Gaussian surface Abundances AI - A new opportunity n-D Calibrations Ideas for the future Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

25. The biggest question… Abundances AI - A new opportunity n-D Calibrations Ideas for the future This mapping is possible if we can define a scale of effective temperature T* using empirical measures ONLY. But how? Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz

26. Ideas for the Future Abundances AI - A new opportunity n-D Calibrations Ideas for the future To find new n-D indicators & improve calibrations of the form: Z=f(c, x1,x2…xn) for HII-like regions and then for AGNs and PNs Find the relation and to test its robustness To investigate finding an empirical scale for T* On behalf of myself, Pepe and Angeles, I would like to thank Guille Hägele, Enrique Perez-Montero and Mariluz Martin for kindly making observational data available and to everyone who has patiently and carefully taken accurate images Many thanks Unravelling the nonlinear physics of high-Z regions with neural networks Mike Taylor, Pepe Vilchez & Angeles Diaz