four kinds of emulators

I wrote in a draft grant proposal related to machine-learning emulators today. I wrote about five different kinds of emulators. Yes I think there are five qualitatively distinct kinds. Here they are:

Full replacement

The most extreme—and most standard—kind of emulator is one that simply replaces the full input–output relationship of the entire simulation. Thus if the simulation starts with initial conditions and boundary conditions, and ends with a final state (after an integration), the full-replacement emulator would be trained to learn the full relationship between the initial and boundary conditions and the final state. A full-replacement emulator is a complete, plug-in replacement for the simulator.

Integrator

Simulation run times generally scale linearly with the number of time steps required to execute the integration. A set of emulators can be trained on a set of snapshots of the simulation internal state at a set of times that is much smaller than the full set of integration time steps. Each emulator is trained to learn the relationship between the internal state of the simulation at one time tA and the internal state of the simulation at a later time tB, such that the emulator can be used to replace the integrator during the time interval from tA to tB. A set of such emulators can be used to replace part or all of the integration performed by the simulator.

Resolution translator

Simulation run times generally scale with the number of grid points or basis functions in the representations of the state. Thus the simulator gets faster as resolution is reduced. An emulator can be trained to learn the relationship between a low-resolution simulation and a matched high-resolution simulation. Then a high-resolution simulation can be emulated by running a fast low-resolution simulation and applying the learned translation.

Physics in-painter

In most physical systems, there are coupled physics domains with different levels of computational complexity. For example, in cosmology, the pure gravitational part of the simulation is relatively low in computational cost, but the baryonic part—the atoms, photons, ram pressures, magnetic fields—is very high in computational cost. The simulator gets faster as physics domains, or equations, or interaction terms, are dropped. An emulator can be trained to learn the relationship between a simulation with some physics dropped and a matched full simulation. Then a full-physics simulation can be emulated by running a partial-physics simulation and applying the learned in-painting of the missing physics.

Statistics generator

In many contexts, the goal of the simulation is not to produce the full state of the physical system, but only certain critical statistics, such as the two-point correlation function (in the case of some cosmology problems). In this case, there is no need to emulate the entire simulation state. Instead, it makes sense to train the emulator to learn only the relationship between the initial and boundary conditions of the simulation and the final statistics of particular interest.

raw data from Cassini

One thing we discovered this past academic year is that NASA Cassini took more than 300,000 images of Saturn's rings! Today I met with Maya Nesen (NYU) and Ana Pacheco (NYU) to look at Cassini raw spacecraft data. Nesen is working on the tabulated housekeeping data, giving the position and orientation of the spacecraft and instruments in various coordinate systems (that we are trying to work out). Pacheco is working on the raw imaging data from the imaging module. We discussed how to display the imaging so that an astronomer can confirm the the noise level and rough noise properties in the pixels. We discussed adjustments to our plots of the housekeeping data to aid in our interpretation of it. In particular, we looked at some of the camera-related meta data and it looks like the camera might have a few different zoom settings. I guess we have to read some documentation!

building trust in emulators

I started writing in a possible grant proposal (that would be in collaboration with others) about the trustworthiness of machine-learning emulators. Emulators are systems that learn the input–output relationship of a computationally expensive simulation and produce (or speed the computation of) new simulation outputs, reducing total computational requirements for a given number of simulations. These are so important now that the ESA Euclid and Simons Observatory data-analysis plans crucially involve emulation.

The issue is: How do we trust that the emulators are giving good outputs? There is no obvious way to test them, except by comparing to held-out training data. But in large-scale structure contexts, no amount of held-out data can test the enormous input data space. I don't know how we will ever trust such systems (and damn do we need to!), but I have some ideas about how to improve the situation. One involves enforcing physics symmetries on the emulators. Another involves running adversarial attacks on them.

truly zero-metallicity stars

All week I have been discussing with Hans-Walter Rix (MPIA) the possibility that we could find the elusive, truly zero metallicity stars in the Milky Way halo. This from an email I wrote today, reacting to the observational point that no-one has ever seen such a star:

How could there be absolutely ZERO zero-metallicity stars in the Milky Way? Here's everything I got:

1. Maybe there are literally no low-mass stars ever made at zero metallicity. Absolutely none, at high precision. This is possible, given how little we know about star formation and the IMF.
2. Maybe stellar evolution is so weird at zero metallicity that low-mass stars go dark by 13 Gyr. I very much doubt that this is a possibility. But maybe low-mass stars at primordial abundances never burn and just slowly collapse into white-dwarf-like condensed objects on a very long cooling timescale. They would be super cold by now, like 100 K maybe??
3. Maybe low-mass stars form slower than high-mass stars in star-forming regions at zero metallicity. This permits a few of the high-mass stars to quickly evolve and explode, polluting the outsides of the just-forming low-mass stars. These low-mass stars would then have low but non-zero surface metallicities, and be very alpha-enhanced. This is possible, although would it really leave NO zero-metallicity low-mass stars behind?
4. Maybe low-mass stars somehow self-pollute at formation (or later in their lives). Maybe the nuclear fusion kicks in slightly before gravitational steady-state or radiative zones are set up, and the first bit of nuclear burning gets mixed in to the stellar envelopes? These stars would appear to have non-zero (but weird, carbon-enhanced maybe?) abundances. Or maybe this happens later in life because of some weird internal mixing. I have literally no idea whether any of this is possible.

elusive quasar dipole

There should be an imprint of the kinematic dipole observed in the cosmic microwave background in any cosmological tracer: The dipole is set by the Solar System barycentric velocity relative to the local Hubble flow, and that same velocity should imprint a dipole on anything cosmological. I have been working on this in part because it is a good measurement to make with Quaia, and in part because the dipole in the quasars is controversial. I have many thoughts, but I will save them for later.

Anyways, Abby Williams (NYU) has been working on making this measurement, and her dipole amplitude and direction depend on what we hold fixed and what we vary (in particular selection-function components), and they also depend on what sky region we use. None of this is surprising; the selection function has a strong dipole in it, and it is not known precisely. But then I don't understand how the studies published previously have such good error bars. Maybe they didn't consider the various different fitting regimes?

finding truly zero-metallicity stars

My conversation with Bergemann (MPIA) yesterday and a conversation with Fouesneau (MPIA) today made me think that it should be possible to do a complete search of the ESA Gaia XP spectra for zero-metallicity (and I mean primordial-abundances) stars. The spectra are easy to compute, and the hypothesis tests against normal stellar models are all set up already in the codes run at MPIA. Let's do this and find the elusive (literally zero membership, apparently) population-III stars in the Milky Way.

convection, granulation, stellar spectra

I had a great and long conversation today with Maria Bergemann (MPIA) about building a model of a full stellar spectrum out of the models they build of small patches of stellar surface, with full 3D convection and full radiative transfer. Their models are sophisticated, and give a full spectrum in every direction from the surface patch. Thus we can integrate a set of patches into a surrogate combined spectrum for one rotating star covered in convecting patches. We discussed how we might do that, technically, and what projects we might then do with the output. What I want to do (yes, you guessed it) is build data-driven models of stellar granulation to improve radial-velocity surveys.

an insight about machine learning

Gaby Contardo (SISSA) completed her visit to Heidelberg today. Over coffee this morning she delivered a very simple, but very nice insight about machine learning outputs. Apologies that this is very Inside Baseball:

As I like to emphasize, you can't really average (or do any populations inferences with) a collection of labels delivered by a discriminative ML method run on a collection of objects. Think: Finding the mean age of a cluster, where each star in the cluster got an age estimate from a discriminative ML method trained on stars with known ages. This is because the discriminative ML methods output something very akin to posterior quantities, and if you average a bunch of posterior estimates, you are multiplying in a prior times itself many times; eventually the prior dominates the inference (in many cases).

Contardo's point: If what you want is a label for a collection of objects, like that mean age, you should train on collections of objects. That is, make a training set where you have sets of N stars, labeled by mean age. Then this model can be applied to a new collection of stars and deliver a mean age estimate! Haha, brilliant. And correct. And consistent with the rules of inference.

mapping the image plane of a spectrograph

I had a phone conversation about wavelength-calibrating the multi-object APOGEE instrument with Karlo de Leon (NYU) today. He has arc images from each night, and line lists for the arc lamps. But before even using the arc lamps, I recommended that he try to find a model for the 2D images that is an outer product of 1D functions: One is the intensity as a function of wavelength from the arc lamp, and the other is the intensity as a function of slit position from the fibers on the slithead.

The thing we realized in the call is that the coordinate system is right when the image is well described as the outer product of these two functions, warped according to that coordinate system! Okay that's nice, now what will the residuals look like? One issue is that there are cosmic rays, hot pixels, and so on. Another issue is that there will be some vignetting that violates the strict outer-product model. We'll address these issues once we get close.

extreme infrared excesses

Gaby Contardo (SISSA) showed up in Heidelberg today to make progress on our project on infrared excesses in normal, non-young FGK stars. Because we are using NASA WISE data (along with ESA Gaia and NASA 2MASS), we are only sensitive to bright, hot infrared excesses, much hotter and brighter than typical debris disks around old stars. We have some candidates, which range in temperature from 300 to 1500 K and are reprocessing maybe one percent or a fraction of a percent of the stellar light. (Warning: I haven't calculated this; this is just a guesstimate based on looking at plots.) What are those things? Today we figured out that they can't be warm substellar companions, so they have to be dust (I guess??).

a likelihood for our Phi-M radio

There are AM radios and FM radios and (if you are a nerd) PCM radios. But Abby Shaum (CUNY) and I have built a Phi-M radio, which demodulates phase variations in a carrier signal. We (with Keaton Bell, CUNY) are using it to find binary companions and planets around stars that show coherent pulsation modes in their photometry. Today I wrote down a noise model for the output of our demodulator. It isn't completely trivial. But it's good, because we can make a likelihood function for fitting our companions. Our model will end up being a limit of the more general model called Maelstrom by Dan Hey (Hawai'i).

using catalogs responsibly

I had a conversation with Vedant Chandra (Harvard) today about how catalogs are used, and how that relates to how they are built. We started off by arguing about how principled one should be about doing a populations inference. Too abstract! So Chandra moved us in the pragmatic direction: Let's look at a very specific inference and see what matters about it. We decided to look at the distances to distant clusters in the ESA Gaia data: How do your inferences depend on the number of stars you use, the signal-to-noise ratios of those stars, and whether your individual-star measurements are maximum-likelihood or obtained by consideration of a posterior pdf? That should answer questions, and set up some concrete points of discussion.

data-driven information

My day started with a conversation with Wolfgang Brandner (MPIA), who asked me how to figure out the information content of ESA Gaia RVS spectra, but in a data-driven way. He wants to avoid the theoretical models at first; that is, he wants to figure out how precisely the spectra contain temperature and metallicity and age information without having temperatures, metallicities, and ages that we believe. One approach is to compare to other data that are sensitve to temperature, metallicity, and age: If the RVS spectra can predict those data, then (conditioned on assumptions) they must contain information about temperature, metallicity, and age. This is similar to questions of risk (or expected error in prediction) in machine-learning contexts.

wobble, star spots, quasar dipole

[Time to try to re-start this forum.]

I spent this morning on three different small activities. One was giving feedback to Matt Daunt (NYU) who is trying to re-build the wobble concept for stellar radial-velocity measurement in jax. He has annoying optimization issues, which are very hard to diagnose! Optimization is always nasty, in my experience.

Another activity was working on the abstract for Lily Zhao's (Flatiron) upcoming paper on stellar variability in the spectral domain, generated by rotating, spotty stars. She is concerned that the paper is too conceptual. I love conceptual papers! I think science moves forward through concepts and implentations, and no individual paper has to do it all.

My third activity this morning was working through the mathematics on a project of Abby Williams (NYU, Caltech) to measure the kinematic dipole in the all-sky Quaia quasar catalog. There are so many different ways to measure it. I think I have a justifiable likelihood function approach, and one in which we could marginalize out—or profile out—the uncertainties in the selection function we have estimated. It's a controversial subject, so I would like to do things correctly.

co-writing

My only real work time today came at the end of the day, working with Emily Griffith (Colorado) on our paper about element abundance ratios in the SDSS-V APOGEE data. We find (like others) that the abundances can be explained pretty precisely with only two processes. My position (contrary to others) is that this is not because there are two dominant kinds of supernovae! It is because the disk mixes gas quickly in the azimuthal direction, such that a star's properties are mainly set by the (cosmic) time at which it was born, and the radius at which it was born. If I'm right, then you can't really use disk stars to understand process yields, since they are always an ugly mixture of processes. If I am wrong, there's lots more to do!