systematics in abundances

I spent part of the weekend looking at issues with chemical abundances as a function of position and velocity in the Solar neighborhood. In the data, it looks like somehow the main-sequence abundances in the APOGEE and GALAH data sets are different for stars in different positions along the same orbit. That's bad for my Chemical Torus Imaging (tm) project with Adrian Price-Whelan (Flatiron)! But slowly we realized that the issue is that the abundances depend on stellar effective temperatures, and different temperatures are differently represented in different parts of the orbit. Phew. But there is a problem with the data. (Okay actually this can be a real, physical effect or a problem with the data; either way, we have to deal.) Time to call Christina Eilers (MIT), who is thinking about exactly this kind of abundance-calibration problem.

what is up with thin-disk chemistry?

Adrian Price-Whelan (Flatiron) and I have been trying to use the chemical abundances of stars to constrain the mass model (or gravitational potential, or orbit structure) of the Milky Way. One thing we have noticed is that the abundances are very sensitive to the coordinate system: If you have the velocity or position of the disk wrong, it is clearly visible in the abundances! That's fun, and motivating. But then we have noticed—and we noticed this two summers ago now—that different elements want to put the disk midplane in different places!

What gives? We have various theories. We started with systematics in the data, but the effects are seen in both APOGEE and GALAH. So it seems like it is real. Is it because relaxation times are very long at small vertical heights? (The disk is like a harmonic oscillator at small vertical amplitudes.) Is it because the thinner disk and thicker disk have inconsistent midplanes? Whatever it is, it seems like it is super interesting. We can't solve this problem in our current paper, but we want to comment on it.

Galactic archaeology

It's a long story, but we have been experimenting continuously with the rules and principles underlying the weekly Stars and Exoplanets Meeting that we run at Flatiron for the NYC astrophysics community. One of the things I say about it is that if you want a meeting to be open, supportive, easy, and community-building, it has to have a strong set of draconian rules! In our most recent set of discussions, we have been talking about theming the meetings around specific science themes. Today was our first experiment with that! Joss Bland-Hawthorn (Sydney) is in town, so we themed the meeting around Galactic Archaeology. We had five short discussions; here are some highlights:

Megan Bedell (Flatiron) showed her incredibly precise 35-element (?) abundance measurements vs stellar age for her Solar twin sample. The abundances are very closely related to the age (for this sample that is selected to have Solar [Fe/H]). Suroor Gandhi (NYU) showed her results on the dependence on dynamical (or really kinematic) actions on [Fe/H] and age for low-alpha and high-alpha stars in the local Milky Way disk. These show that the two different sequences (high and low alpha) have different origins. And Rocio Kiman (CUNY) showed her M dwarf kinematics as a function of magnetic activity that could be used to constrain a disk heating model. All three of these presentations could benefit (for interpretation) from a forward model of star formation and radial migration in the Milky Way disk, along with heating! This is related to things I have done with Neige Frankel (MPIA) but would require extensions. Simple extensions, though.

Adam Wheeler (Columbia) showed us abundances he has measured all over the Milky Way from LAMOST spectroscopy, training a version of The Cannon with GALAH abundances. It's an amazing data set, and he asked us to brainstorm ideas about what we could do with it. He seems to have features in his catalog that look similar to the midplane issues that were causing me existential angst this past August. Bland-Hawthorn said that he sees similar things in the GALAH data too.

And Bland-Hawthorn himself talked about the possibility that some future instrument could measure stellar accelerations and get the Milky Way acceleration field directly! He started by commenting on the conclusions of the Bonaca et al work on a possible dark-matter perturber acting on the GD-1 stellar stream. His remarks played very well with things Bonaca and I have been discussing around making a non-parametric acceleration map of the Milky Way.

In summary: A great experiment!

GD-1 and chemical tangents

Tuesdays and Thursdays are lower on the research this semester! But I did get in two excellent discussions. The first was with Bonaca (Harvard) who has made an absolutely great visualization that compares the Gaia data on GD-1 and her model for GD-1. I think this figure might get featured in a lot of talks! We are still checking things, but it looks great. We discussed what would be the final scope of her paper, because—as with all projects—there is a huge possible scope but we need to finish a paper soon! I'm happy with the scope and it seems achievable and sensible. The big issue is that the constraints we have on the perturber than interacted with GD-1 come from a model that has toy aspects to it, while the full generative stream model is expensive enough that we don't want to go there for inference just yet. Soon, but not for this paper.

Over a late lunch I discussed many things with Price-Whelan (Princeton), both about GD-1 and about our chemical tangents project. On the latter, we discussed (for approximately the millionth time) how to describe the project most compactly. This project is strange enough for the typical astronomer, that we have to think carefully about how we present it. There are a lot of things that sound right but are wrong. And I am a huge believer in repeatedly re-describing projects. I think every time you go through it, you learn something new, and improve your presentation. This is a huge benefit of fully Open Science.

In that spirit: We are trying to find the surfaces in phase space along which the distribution of stars in abundance space is constant. Not the abundance is constant, but the distribution in abundances. Those surfaces contain the orbits! In some sense it comes down to the point that the joint distribution in actions and abundances is not separable, so the abundances can inform you about the actions! But that description is too terse. And Rix likes to say: Stars don't change their abundances as they orbit! So if you have drawn orbits through phase space that would require abundance changes, either your population isn't mixed or else you are wrong about those orbits.

how to describe my current project

My flight home got seriously delayed and I had an extra day in Aspen. I spent it talking about (and working on) my project to infer dynamical invariants in the well-mixed parts of the Milky Way from chemical (element-abundance) invariants. I had various epiphanies and useful discussions:

Rix (MPIA) and I worked on how you explain the project to the world. One explanation is this: In addition to dynamical invariants, there are chemical abundances, which depend on the dynamical invariants (and not on the conjugate angles). Therefore inference of the dynamical invariants must be better or improved if you model the abundance invariants as well or in tandem. Another explanation is this: Imagine you do a dynamical inference (like Jeans modeling) and you (effectively) determine orbit structure. If you are slightly off, the element abundances you have measured will reveal the issues, and can be used to adjust or update or improve the orbit-structure inference, because stars don't change their abundances as they orbit!

Price-Whelan (Princeton) and I worked on how to compare the project with Jeans modeling, Schwarzschild modeling, or fully marginalized forward modeling of the kinematics (which has almost never been done). I have a scaling argument that my new method must be better than any of these: Each of these methods gets some amount of information out of the positions and velocities of the stars. My chemical-tangents method gets more information from every new element abundance you measure (even if each new element is fully covariant physically with the ones you have measured before; it is the measurements that are near-independent). So in some limit (and I think that limit arrives very early), it will have more information than any of these methods. But of course I need to demonstrate this quantitatively in the very near future.

Another point of comparison is related to the conditional or generative or causal structure of the model: I am modeling the abundance distribution conditioned on the phase-space positions. This means that I don't need to know the selection function of the survey, which Jeans modeling does (to some extent) and the more serious methods do (to great precision). On the other hand, because I am conditioning on the positions and not generating them, I can't (gracefully) account for measurement uncertainties in position. (Of course that's true for Jeans too.)

Anyway, the reason I am writing all this is because: The best practice for writing (the paper) is writing (this blog and emails and etc).

Aspen, day 4

Adrian Price-Whelan (Princeton) resolved some of our code differences today as unit or dimensions differences. That was good! But we still have the problem that different elements (in comparison with kinematics) lead to different inferences about orbits in the Milky Way disk. Don't know what to do about that! Either the data are wrong, or there is a big discovery here.

Ana Bonaca (Harvard), Price-Whelan, and I discussed how to build a pseudo-likelihood for comparing the models that Bonaca has for a stream perturbation to the real data. This is a bit of a hard problem, because we want objectives that improve as the agreement improves, but we don't want to build a fully generative model of the data. Why not? because we don't have a good generative model, and perturbations away from a bad generative model could lead to very wrong inferences. All we want, after all, is a rough sense of what kinds of events are consistent with the data.

In the afternoon, I gave the Aspen Center for Physics Colloquium. I spoke about Gaia and dark matter, but I also threw in my thinking about the inference of Solar System dynamics in the 17th Century: We would do it very differently now! I have much more to say but I am too tired to write it here.

Aspen, day 3

Side by side, Price-Whelan (Princeton) and I worked through and discussed code inconsistencies between my code and his code to compute the likelihood function for my chemical-tangents (working title) project, that uses chemical invariants to find dynamical invariants. It was a frustrating discussion, because we couldn't figure out either the issues or how to test. That's our project for tomorrow!

Bonaca (Harvard) reported in: She can show that the gaps and associated loops we find in the GD-1 stream cannot be caused by interaction with a molecular cloud on a disk orbit! That means that the only explanation remaining is dark-matter substructure. Awesome! I'm stoked!

Aspen, day 2

After I found an insanely huge and existential bug in my code, Price-Whelan (Princeton) and I did a full code review of my project that takes advantage of chemical-abundance invariance to determine dynamical invariants. The big issue is that the action computation is expensive; it involves some kind of integration or quadrature. As we were discussing this, Eugene Vasiliev (Cambridge) joined us and suggested ways to speed up the action calculation using the energy invariant to aid in the integration.

[Insert tire screeching noise] We don't need actions! We only need some kind of invariant for this project. Indeed, I have tried various different invariants and they all work equally well. So we can use the energy invariant, which requires no integration! Woah, and thanks Vasiliev! That sped up the code by factors of many hundreds, which we then partially compensated down by doing more complete MCMC samplings. But development cycle is far improved.

I also had a great planning session with Bonaca (Harvard) where we worked out coordinate systems and methods for making far more realistic our project to model the GD-1 stream gaps. We are modeling one of the gaps and spurs with a dark-matter (or really dense-object) interaction. We needed to make things far more realistic, because we want to rule out disk-passage events as gap causes. That requires that we have GD-1 orbiting in a Galaxy with a disk and the observer (us) in the right places at the right times. Things are complicated, because everything happens on the kinematic equivalent of the past light cone—the past star cone?

Aspen, day 1

I'm in Aspen for the week, working on Milky Way dynamics and chemical abundances. The day started with introductions, in which many themes arose. One is that detailed abundances are here, are good, are numerous, and are under-utilized. So the work I am doing fits in pretty well! It occurred to me (Duh!), when some of the more particle-oriented people spoke, that imaging the dark matter is no different from testing gravity, at least conceptually. So I can spin off a testing-gravity side project.

The MCMC runs I sent off working on my laptop on Friday did not disappoint: I got amazingly strong constraints on the dynamics of the disk, including a percent-level measurement of the disk density! That's a precision of course; at percent level none of my assumptions are defensible. But it works really well: The iso-chemical contours really do show you the orbits, and precisely.

But, the most interesting respect in which my assumptions are violated is that the different elements want to put the midplane of the disk in different locations! Huh? And the effect is just clearly visible in the GALAH data. Rix (MPIA) pointed out today that the phase-mixing times can be long near the disk center because in the limit of a harmonic potential, all frequencies are degenerate and mixing doesn't happen. So maybe we have clear evidence for non-phase-mixing, vertically, in the disk. Or of course maybe there are (very adversarial, I might say) issues with the GALAH data. But the nice thing is you can just see it in the element abundances. Look for yourself: The midplane in [Fe/H] looks different from the midplane in [Si/Fe]. (Plots have z-velocity on the horizontal axis and z-position on the vertical axis).

bad development cycle is bad

My day started with a conversation with Christina Eilers (MPIA) about the Milky Way rotation curve. We found some strange kinematics points that might be messing with us, and realized that they are almost all stars at or past the Bulge, and therefore not affecting our results, which are only for Galactocentric radii greater than 5 kpc, to avoid the craziness of the bar (which violates our dynamical assumptions). Her figures are ready, so I encouraged her to write figure captions and assemble the paper.

I spent my research time getting MCMC running on my Chemical Tangents project. I have a marginalized likelihood, so all I had to do is put on priors and insert into emcee. Oh how I would have benefitted from a testing environment! When I packaged it all up for emcee I messed up the units of almost all the inputs, so I got garbage in every MCMC run. And the runs took a long time, so diagnosis was painful. Unit testing. And for units! Live and fail to learn, that's what I say.

Once everything appeared to be working, I set up some (nasty) multi-processing, set my laptop to stay awake all night, and blew processes. I should have converged samplings by morning.

best constraints on disk dynamics ever

In my Chemical-Tangents project (working title only), I am modeling the abundance distribution as a function of dynamical actions to determine the shapes of the orbits in phase space, or, equivalently, the force law or the density distribution or the potential. I have parameters for the force law but also for the abundances and their variation. I spent the morning figuring out how to marginalized out those abundance parameters, which are nuisances (for my purposes). I got it working; much of it is even analytic (so I only have to do one numerical integral per element ratio).

I then ran on everything, and I find that I have the best constraints on the Milky Way disk dynamics, ever! That is, on the kinematic location of the midplane, the scale height of the mass distribution, and the central or mean density. I am pretty stoked: Each abundance ratio individually gives good constraints on these parameters, and their combination will be exceedingly constraining. So I am pretty confident that I have a great project. My next job is to put this all into a sampler (like emcee, which is good for low-dimensional problems) and sample it.

dynamics, abundances, and a likelihood function

In an undisclosed location off the grid I worked on my code to leverage element-abundance invariances of stars (in the GALAH Survey) to deliver dynamical invariants. I switched from a non-parametric abundance model that put the stars into abundance bins to a parametric model which makes the abundances a smooth function of actions. I also improved my action-computing code and built an interpolator to speed things up. And suddenly my likelihood function got really smooth, and it peaks at sensible dynamical parameters for the Milky Way disk! So I have a project. Note that the way I am operating is to work on the likelihood function until I can see that it behaves sensibly on slices (lines in parameter space) and only then will I think about the inference more generally.

After that success, I tweaked code, ran stuff, and started making an outline of the hard parts of the paper I need to write.

The Cannon again, chemical tori

Within one frantic half-hour, Eilers (MPIA) and I completely implemented a new version of The Cannon and ran it on her sample of luminous red giants. We did this so that we can compare the internals of her linear model for parallax estimation to the internal derivatives or label dependencies for The Cannon. This will let us take a step towards interpreting the internals of the spectrophotometric-parallax model. We scanned the comparison but it doesn't look quite as easy to interpret as I had hoped.

As soon as this was done, I said some words in MPIA Milky Way group meeting about my ideas for Chemical Tangents: That is, the idea that orbits must lie in the level surfaces (hyper-surfaces in 6-d phase space) of the chemical abundance distribution. The method puts an enormous number of constraints on the orbit space, so it has the potential to be extremely constraining. Rix (MPIA) is suspicious that it all sounds too good to be true: The method requires no knowledge of the selection function (to zeroth order) and no second-order statistics. It is entirely first-order in the data. Damn I hope I'm not wrong here.

In the morning, Rene Andrae (MPIA) showed me his enormous cross-match of spectroscopic surveys that he is putting together in part to understand the stellar parameter pipelines of Gaia (to which he is a contributor). He has the input data for a combinatoric diversity of projects we could do with The Cannon or stellar-parameter self-calibration.

hike-writing and hike-coding

I was off the grid for a few days, but I took opportunities when others were hiking to sit at the Hütte and do some writing in the spectroscopic-parallax (or spectroscopic estimates of luminosity and distance) project. I have structured the paper in our new style, which is to lay out all assumptions clearly at the beginning and then find the method that flows from those assumptions. If no method flows, new or different or additional assumptions are needed. This makes the subjectivity clear, but also protects us from the complaint that there are implicit assumptions. A referee can object to the assumptions but (we hope) not the method given the assumptions.

I also worked out with Adrian Price-Whelan (Princeton) the details of the simplest possible inference of dynamics from element abundances. The idea is to find the dynamical model that makes the abundances a function (only) of the dynamical actions (or other invariants). For the demonstration project, we are just going to do vertical dynamics, and just with very simple moments of the abundance distribution. I built and tested a leap-frog integrator to integrate the vertical orbits.

angles mixed?

I spent a few days fully off-grid, hiking. During that time I nonetheless thought and dreamed about some astrophysics projects. Not sure if that's healthy! But hey.

In particular, Hans-Walter Rix (MPIA) and I talked out some possible projects with Gaia DR2 that could make good use of action–angle formalism to constrain properties of the Milky Way. For example, we could look at angle uniformity in action boxels. That requires a selection function, but maybe one is forthcoming? For another, we could look at whether angles predict element abundances at fixed actions? If they do, then either the potential is wrong or the populations are kinematically young. And for another, we could look at point symmetries in velocity space (where selection should be simple) of stars in action boxels. Any asymmetries point to dynamically young populations. All projects to discuss with the team on my return to civilization.

detailed abundances of pairs; coherent red-giant modes

In the morning I sat in on a meeting of the GALAH team, who are preparing for a data release to precede Gaia DR2. In that meeting, Jeffrey Simpson (USyd) showed me GALAH results on the Oh et al comoving pairs of stars. He finds that pairs from the Oh sample that are confirmed to have the same radial velocity (and are therefore likely to be truly comoving) have similar detailed element abundances, and the ones that aren't, don't. So awesome! But interestingly he doesn't find that the non-confirmed pairs are as different as randomly chosen stars from the sample. That's interesting, and suggests that we should make (or should have made) a carefully constructed null sample for A/B testing etc. Definitely for Gaia DR2!

In the afternoon, I joined the USyd asteroseismology group meeting. We discussed classification of seismic spectra using neural networks (I advised against) or kernel SVM (I advised in favor). We also discussed using very narrow (think: coherent) modes in red-giant stars to find binaries. This is like what my host Simon Murphy (USyd) does for delta-Scuti stars, but we would not have enough data to phase up little chunks of spectrum: We would have to do one huge simultaneous fit. I love that idea, infinitely! I asked them to give me a KIC number.

I gave two talks today, making it six talks (every one very different) in five days! I spoke about the pros and cons of machine learning (or what is portrayed as machine learning on TV) as my final Hunstead Lecture at the University of Sydney. I ended up being very negative on neural networks in comparison to Gaussian processes, at least for astrophysics applications. In my second talk, I spoke about de-noising Gaia data at Macquarie University. I got great crowds and good feedback at both places. It's been an exhausting but absolutely excellent week.

noise, calibration, and GALAH

Today I gave my second of five Hunstead Lectures at University of Sydney. It was about finding planets in the Kepler and K2 data, using our non-stationary Gaussian Process or linear model as a noise model. This is the model we wrote up in our Research Note of the AAS. In the question period, the question of confirmation or validation of planets came up. It is very real that the only way to validate most tiny planets is to make predictions for other data. But when will we have data more sensitive than Kepler? This is a significant problem for much of bleeding-edge astronomy.

Early in the morning I had a long call with Jason Wright (PSU) and Bedell (Flatiron) about the assessment of the calibration programs for extreme-precision RV surveys. My position is that it is possible to assess the end-to-end error budget in a data-driven way. That is, we can use ideas from causal inference to figure out what parts of the RV noise are coming from telescope plus instrument plus software. Wright didn't agree: He believes that large parts of the error budget can't be seen or calibrated. I guess we better start writing some kind of paper here.

In the afternoon I had a great discussion with Buder (MPIA), Sharma (USyd), and Bland-Hawthorn (USyd) about the current status of detailed elemental abundance measurements in GALAH. The element–element plots look fantastic, and clear trends and high precision are evident, just looking at the data. To extract these abundances, Buder has made a clever variant of The Cannon which makes use of the residuals away from a low-dimensional model to measure the detailed abundances. They are planning on doing a large data release in April.

#ken75, day 1

Today was the first day of the meeting Galactic Archaeology and Stellar Physics in honor of Ken Freeman (MSSSO). As per usual when I am at a meeting, this blog can't convey the full day of talks, so I will just put here very personal highlights.

Freeman opened the conference, giving his overview of what he wants to know about the Galaxy. He is excited about the revolution happening now in which we might have 6-d phase space and 30-ish chemical abundances for stars all over the Galaxy. He brought up two themes that would be very important in today's talks, the bimodality in the alpha/Fe distribution (and its connection to different disk components), and radial migration. On the former, he uses the bimodality to separate the thin and thick disks; he is so confident that he literally calls a chemically separated component the “thick disk”. On the latter, he showed some results I hadn't seen on velocities as a function of metallicity that he argued make the radial migration clear. I have to figure that out! Relevant to things we worked on in the Gaia Sprint, he asked whether the disk components are different heights because of heating or a big event. I think we now know that at small heights it is heating. But the alpha-rich component might be thick because of an event.

Hekker discussed the SAGE project to get a uniform catalog of masses and ages for stars out of non-uniform inputs. She referenced The Cannon but is taking an opposite tack: She is trying to homogenize the data by making all the data constrain the same physical model.

Ruiz-Dern discussed red-clump stars, and in particular building a data-driven model of the relationships between spectroscopic parameters and photometric colors. She showed very good evidence that we could do a lot of the science we do with spectroscopy with photometry instead! That was not her goal, but it got me thinking in a totally new way about my project with Lauren Anderson.

Bovy discussed his results of dissecting the Galaxy into narrow chemical-abundance slices. Where Freeman had used the differing amplitudes in the alpha/Fe bimodality as a function of position to show how different different parts of the Galaxy are, Bovy used the same data to show how similar different parts are! That's a great property of a good scientific result: It can be interpreted either way! He discussed in detail what aspects of his Galaxy decomposition results are consistent and inconsistent with ideas from radial migration.

Talks by Duong and Chiappini again used chemistry to investigate the thin and thick disks, and Chiappini explicitly warned the audience that we will get different results if we split the Galaxy on chemical or structural lines. This also mirrored comments by Bovy.

Toyouchi looked at explaining the alpha/Fe bimodality with an event in the Milky Way's past. This got me thinking about the question: How can we tell whether the bimodality is a fundamental property of the chemical enrichment of molecular clouds or whether it is just the result of some very specific event in the Milky Way's particular past?

Feuillet showed amazing age-abundance relationships for the 19-ish elements that APOGEE observes. It is a goldmine of empirical results. She finds a few highly problematic elements. Like us, she finds that alpha/Fe is strongly correlated with age, at all alpha/Fe values and at all ages.

Buder talked about the GALAH survey and what has been learned and improved with the Gaia DR1 TGAS release. He announced that GALAH is using The Cannon as part of its data analysis pipeline. He said (and I believe him) that they are using it to speed up the code. I like that; it's good for my brand!

stars have simple spectra! The Cannon

Christina Eilers (MPIA) and I spent a long time today pair-coding her extension to The Cannon in which we marginalize over the true labels of the training data, under the assumption of small, known, Gaussian, label noise. Our job was to vastly speed optimization by getting correct derivatives (gradient) of the objective function (a likelihood function) with respect to parameters, and insertion of this into a proper optimizer. We built tests, did some experimental coding, and then fully succeeded! Eilers's Cannon is slower than other implementations, but more scientifically conservative. We showed by the end of the day that the model becomes a better fit to the data as the label variances are made realistic. Stars really do have simple spectra!

While we were working, Anna Y. Q. Ho and Sven Buder (MPIA) were discovering non-trivial covariances between stellar radial Velocity (or possibly radial velocity mis-estimation) and alpha abundances, with Ho working in LAMOST data and Buder working in GALAH data. Both are using The Cannon. After some investigation, we think the issue is probably related to the collision of alpha-estimating spectral features and ISM and telluric features. We discussed methods for mitigation, which range from censoring data at one end and fully modeling velocity along with the model parameters at the other.

Late in the day, I finished my response to referee and submitted it.

projects with The Cannon

I got troubled this morning by the so many projects problem! In the subdomain of my life that is about modeling spectra of stars, and within that the subdomain that is thinking about APOGEE data, there are these, which I don't know how to prioritize!

• Fit for velocity widths and velocity offsets (redshifts) simultaneously with the star labels, to remove projections of velocity errors and line-spread-function (or microturbulence) variations onto parameters of interest.
• Fit stars as linear combinations of stars at different velocities to find the double-lined spectroscopic binaries. Combine this with Kepler data to get the full properties of eclipsing binaries. We have many examples, and I expect we will find many more! We might put Adrian Price-Whelan onto parts of this this week.
• Build (train) models for all parts of the H-R diagram, especially the subgiant and dwarf parts, where we have never produced good models. These are particularly important in the era of Gaia. We might convince Andy Casey to do some of this this week, and Sven Buder (MPIA) is also doing some of this in GALAH.
• Project residuals onto (theoretically determined) derivatives with respect to element abundances, to get or check element abundances. This might also be used to build an element-abundance measuring system that doesn't require a full training set of abundances that we believe. Yuan-Sen Ting (UCSC) is producing the relevant derivatives right now.
• Marginalize out noisy labels at training time, and marginalize out noisy internal parameters at test time. We have Christina Eilers (MPIA) on that one right now.
• Look at going fully probabilistic, where we get posteriors over all labels and all internal parameters. I owe Jonathan Weare (Chicago) elements for this.
• Include photometry into the training and test data to break the temperature–gravity degeneracies. And maybe also extinction! This is easy to do and ought to have a big impact.
• Include priors on stellar structure and evolution to prevent results from departing from physically reasonable solutions. This is anathema to the stellar spectroscopy world (or most of it), but much desired by the customers of stellar parameter pipelines!
• Add in latent variables to capture variations in stellar spectra not captured by the quadratic-on-labels model. Are the learned latent variables interpretable?