Structure determination in astronomy and astrophysics

How it is used

Almost nothing in astronomy is measured directly. A telescope records light arriving at a detector, and the quantity of interest, the mass of a cluster of galaxies, the pull of gravity inside a galaxy, the temperature of a star, has to be inferred from it. Structure determination is that inference: going from the measurement back to the thing that produced it. Machine learning enters as the step that performs the inversion. A network is shown many simulated examples where the hidden structure is known, because a simulation produced it, and learns to read the structure out of the measurement. Once trained, it can be applied to real observations of the same kind.

The examples here show several shapes this takes. One trains a convolutional network, a model that scans an image for local patterns, on maps of how the shapes of distant galaxies are stretched by the mass lying in front of them, in order to recover the mass. Another fits flexible probability models to the positions and velocities of stars in a simulated galaxy, producing a smooth, differentiable description of how those stars are distributed from which the gravitational pull can be derived. A third classifies the type of a star from a single wide-band image, using the subtle way colour changes the shape of the blur a telescope imposes. A fourth builds the forward model itself so it can be differentiated, letting the initial conditions of a cosmic structure be fitted directly.

Why researchers use it

The classical inversions are either unstable or expensive. Recovering mass from lensing means undoing a smoothing operation, which amplifies noise, so traditional methods blur the result and lose small structure. Recovering a gravitational potential from a snapshot of stars means estimating a distribution in six dimensions, three of position and three of velocity, from a finite sample, which binning handles badly. A trained network absorbs much of this difficulty into the training stage: the hard work is done once, on simulations, and the result is applied cheaply to data. Where the simulation is good, the model also learns the noise and the survey's quirks rather than having them treated as an afterthought.

The second reason is that these models are smooth and differentiable, meaning gradients can be taken through them. That matters because it lets a structure be fitted rather than merely guessed at: the model can be nudged, step by step, towards agreement with the data, even when the structure has as many unknowns as there are pixels or particles. It also lets a quantity that is awkward to measure, such as the force field implied by a distribution of stars, be obtained by differentiating something the model already represents. In effect, the network stands in for a hand-built physical model that would be too rigid, or for an estimator that would be too noisy.

In the record

astronomyNeural network turns galaxy shape distortions into maps of invisible cluster massA convolutional network recovered cluster mass maps from simulated galaxy shape catalogues, taking mean ellipticity components and measurement error as image channels, with no smoothing applied first.astronomyNeural networks recover a simulated barred galaxy's gravity from one snapshotChains of continuous normalizing flows were fitted to tracer particles in concentric shells of a simulated barred galaxy, giving a smooth, differentiable six-dimensional distribution.astronomyClassifying stars by type from a single wide-band telescope imageA convolutional encoder turned single-band star images into a short feature vector, which a small network mapped to one of thirteen spectral classes.astronomyReconstructing the early universe's density field with a smoothed map of cosmic structureA differentiable forward model generated a mock catalogue of tracer counts from a Gaussian initial field, then the same model was used to infer that field back.

Limits

These models learn from simulations, so they inherit whatever the simulation assumes about physics, noise and survey conditions, and may fail quietly on real data that differs. Where a study tests on mocks made by the same forward model used for inference, success shows the method is self-consistent, not that it matches the sky. A network trained at one depth, resolution or source density need not transfer to another. Most produce a single best estimate rather than an honest range of possibilities, and the recovered structure can look sharper and more certain than the data support.

Written by AIxSci: the background from general knowledge, the examples from checked records.