blasé: An interpretable transfer learning approach to cool star échelle spectroscopy

Comparison of échelle spectra to synthetic models has become a computational statistics challenge, with over ten thousand individual spectral lines affecting a typical cool star échelle spectrum. Telluric artifacts, imperfect line lists, inexact continuum placement, and inflexible models frustrate the scientific promise of these information-rich datasets. Here we debut a scalable machine-learning framework "blasé" that addresses these challenges. The semi-empirical approach can be viewed as "transfer learning"--first pre-training models on noise-free precomputed synthetic spectral models, then learning the corrections to line depths and widths from noisy whole-spectrum fitting. The auto-differentiable model employs back-propagation, the fundamental algorithm empowering modern Neural Networks. Here, however, the 40,000+ parameters symbolize physically interpretable line profile properties (amplitude, width, location, shape) plus RV and vsini, rather than difficult-to-interpret neural network "weights". This hybrid data-/model- driven framework allows joint modeling of stellar and telluric lines simultaneously, a potentially transformative step forwards for pesky telluric mitigation in the near-infrared. Blasé also acts as a deconvolution tool. It is suitable for Doppler Imaging scenarios with longitudinally symmetric surface features like bands or polar spots, which evade detection in differential techniques. Blasé can also create super-resolution semi-empirical templates useful for critically evaluating atomic and molecular line lists. Its sparse-matrix architecture and GPU-acceleration make blasé fast, with end-to-end training of 50+ échelle orders in under 1 minute. The open-source PyTorch-based code (blase.readthedocs.io) includes tutorials and API documentation. We show how the tool fits into the existing Python spectroscopy ecosystem, demonstrate a range of astrophysical applications, and discuss limitations and future extensions.

Transcript

1. blasé A transfer learning approach to échelle spectra Michael Gully-Santiago The University of Texas at Austin Machine Learning for Cool Stars Splinter Session Cool Stars 21 July 5, 2022
2. blasé is a general purpose experimentation framework aimed primary at high bandwidth, high-resolution vis/near-IR spectra X-shooter CRIRES+ APOGEE IGRINS HPF UVES iSHELL NEID HARPS MAROON-X CARMENES VELOCE Keck NIRSPEC HRS etc…
3. blasé is a general purpose experimentation framework aimed primary at high bandwidth, high-resolution vis/near-IR spectra IGRINS HPF (this talk) Park et al. 2014 Mahadevan 2012
4. blasé
5. The problem with échelle spectra: The mere act of comparing an échelle spectrum to a model becomes a computational statistics challenge. • Voluminous data • Imperfect models • Confounding factors (tellurics) + • In f lexible models (~4 parameters in a typical grid) • Expensive models
6. Stellar spectral models are imperfect. Missing lines; under-/over- predicted depths, widths, shapes, locations. λ (Å)
7. The model and data are voluminous. A typical HPF/IGRINS spectrum of a K/M dwarf contains >10,000 stellar lines.
8. (In some places worse than others.) Telluric absorption confounds the stellar spectrum.
9. Four modern solutions to (aspects of) these problems: github.com/Star f ish-develop/Star f ish github.com/HajimeKawahara/exojax Czekala et al. 2015 Starfish wobble Bedell et al. 2019 github.com/megbedell/wobble exojax Kawahara et al. 2022 FAL Cargile et al. (in prep) github.com/pacargile/FAL (See also ThePayne by Phill Cargile)
10. wobble Bedell et al. 2019 github.com/megbedell/wobble github.com/HajimeKawahara/exojax exojax Kawahara et al. 2022
11. wobble Bedell et al. 2019 github.com/megbedell/wobble github.com/HajimeKawahara/exojax exojax Kawahara et al. 2022 more data-driven more model-driven more parameters (~105) fewer parameters (~15) more precise better out-of-band prediction accuracy
12. wobble Bedell et al. 2019 github.com/megbedell/wobble github.com/HajimeKawahara/exojax exojax Kawahara et al. 2022 more data-driven more model-driven “Hybrid” github.com/gully/blase blasé Gully-Santiago & Morley (in prep)
13. wobble Bedell et al. 2019 github.com/megbedell/wobble github.com/HajimeKawahara/exojax exojax Kawahara et al. 2022 github.com/gully/blase blasé Gully-Santiago & Morley (in prep) underlying machine learning frameworks:
14. underlying machine learning frameworks: machine learning frameworks provide GPU acceleration and automatic differentiation* For a tutorial of autodi ff , Jacobians, and Hessians applied to spectroscopy, see: github.com/gully/TgiF *c.f. Gunes-Baydin et al. 2015 for a review ArXiV: 1502.05767
15. Key idea A typical echelle spectrum has: Nlines } ( 𝛌 c , A, 𝛔 , 𝛄 ) Line center Amplitude Gaussian width Lorentzian width Four parameters for all 10,000 spectral lines
16. Key idea A typical echelle spectrum has: Nlines } ( 𝛌 c , A, 𝛔 , 𝛄 ) Line center Amplitude Gaussian width Lorentzian width Four parameters for all 10,000 spectral lines blasé f its all 40,000 parameters simultaneously with autodi ff . = 40,000 total parameters
17. Step 0 Pick closest stellar model template to your target of interest: Te = 4700 K logg = 4.5 [Fe/H] = 0
18. Step 1 Place a coarsely-tuned Voigt pro f ile at the location of all lines.
19. Step 1 Optimize all 40,000 line parameters simultaneously.
20. Step 0.5 (optional) Pick closest telluric model template to your time of observation: Tobs = 17° C Humidity = 40% Gullikson et al. 2014: TelFit
21. Step 1.5 (optional) Place a coarsely-tuned Voigt pro f ile at the location of all lines. Gullikson et al. 2014: TelFit
22. Step 1.5 (optional) Optimize all 12,000 telluric line parameters simultaneously. Gullikson et al. 2014: TelFit
23. Clone the spectra Step 1 Apply vsini & RV Step 2 Step 0 Choose Templates Multiply by telluric Step 3 Instrument convolve & resample Step 4
24. Clone the spectra Step 1 Apply vsini & RV Step 2 Step 0 Choose Templates Multiply by telluric Step 3 Instrument convolve & resample Step 4 Compare to data Step 5 RV, vsini, and all stellar and telluric line properties are tuned simultaneously.
25. Before λ (Å)
26. λ (Å) After
27. blasé learns a super-resolution template. before λ (Å)
28. blasé learns a super-resolution template. after λ (Å)
29. 56 s End-to-end HPF whole-spectrum f itting on NVIDIA RTX 2070 GPU. GPUs, sparse matrices, and approximations yield huge speedups. blasé is fast. End-to-end HPF whole-spectrum f itting on M1 MacBook Air (CPU only). 1h15m
30. Key idea: Sparsity We use sparse matrices* in PyTorch to achieve 100x speedups. *c.f. Saad 2003
31. Main challenge: Regularization We face a bias/variance tradeo ff . c.f. Bedell et al. 2019 In fi nite regularization No regularization Laissez-faire: Surrealist over fi tting No learning: recover the input template
32. Main challenge: Regularization We face a bias/variance tradeo ff . c.f. Bedell et al. 2019 In fi nite regularization No regularization Laissez-faire: Surrealist over fi tting No learning: recover the input template “Sweet spot” Regularization encodes our intuition: Line properties should match PHOENIX unless there’s enough data to say otherwise
33. What’s possible? blasé serves as a foundation for many new strategies. 1. Doppler Imaging with imperfect templates (Luger et al. 2021) • Zonal bands (Cross f ield et al. 2014) • Polar spots (Roettenbacher et al. 2017) 2. Starspot spectral decomposition (Gully-Santiago et al. 2017) 3. Spectroscopic binary joint modeling (Czekala et al. 2017) 4. Automatic equivalent width tabulation 5. Discover “true” lineshapes with hidden neural network layers 6. Spectral calibration across the grid dimensions (c.f. previous talk by Bello-Garcia) 7. Brown Dwarfs with non-parametric pseudo-continuum (e.g. GPyTorch) 8. Adapt the templates to magnetic f ields / Zeeman effect 9. Provide quantitative feedback to modelers at native resolution
34. blasé is open source. We have tutorials, deep dives, FAQs, and API documentation. blase.readthedocs.io
35. blasé is open source. We have tutorials, deep dives, FAQs, and API documentation. blase.readthedocs.io
36. blasé is user-friendly. It serves as a gentle introduction to key concepts in ML for newcomers. blase.readthedocs.io
37. blasé is a work in progress, we invite your help: Engage with us on GitHub Issues and more. github.com/gully/blase
38. Typical spectral analysis work f low with blasé blasé 2D echellogram reduction pipeline 1D spectrum post-processing Initial spectral template selection Spectral f itting or wobble or starfish or … muler 🆕 gollum 🆕 Gully-Santiago et al. 2022; JOSS github.com/OttoStruve/muler github.com/BrownDwarf/gollum
39. blasé • blasé offers an interpretable model for echelle spectra, including tellurics. • It leverages the key enabling technology autodiff to achieve excellent precision. • By using Sparse Matrices and GPUs we achieve excellent computational performance. • It has tons of conceivable extensions. • We have also made ancillary tools muler and gollum for lowering the barrier to entry. • Altogether these codes form an easy-to-use ecosystem for end-to-end spectral analysis.
40. The end.