Gaussian process in materials and computational chemistry

How it is used

Materials science and computational chemistry try to link what a substance is made of, and how its atoms are arranged, to what it does: how hard it is, how it conducts, how it reacts. The honest way to find out is to make the material and measure it, or to solve the quantum mechanics of its electrons on a computer. Both are slow, so only a small number of candidates can ever be tried. A Gaussian process is a statistical model that fits a curve through the few results already in hand and, at every untried point, returns both a guess and an estimate of how unsure that guess is.

In practice the model sits between the researcher and the expensive step. Each material is first turned into a list of numbers: average properties of the elements in it, or a description of the local geometry around each atom. The Gaussian process is fitted to the measured or computed values for those lists, then asked about everything not yet tried. Its uncertainty is used to pick what to do next, and the new result is added and the fit redone. The same machinery can predict energies and the forces on atoms, which is what a structure search or a simulation needs.

Why researchers use it

Researchers reach for it because the datasets here are small and costly, and a model that only guesses is not enough. The uncertainty is the useful part. It tells you where the model is confident, so you can trust it, and where it is guessing, so that is where the next experiment or quantum calculation is worth spending. That turns a blind sweep through a composition space into a loop that chooses its own next sample, and lets a search stop when nothing untried looks either promising or unknown.

It also stands in for the expensive calculation itself. Quantum chemistry gives energies and forces for one arrangement of atoms at a time; finding a stable structure may need thousands of such arrangements. A fitted model answers in a moment, so the search can wander cheaply over the surrogate and fall back on the real calculation only at the few points that matter. Physical knowledge can be written into the model as well, through the choice of input description or a prior that encodes what is already expected, so the small dataset is not asked to carry everything.

In the record

materials-chemistryMachine learning picked which shape-memory alloys to make next, round by roundA Gaussian process, alongside support vector regression, was fitted to measured alloys to map six composition-weighted elemental features onto thermal hysteresis.materials-chemistryPretrained potentials give a structure search a head start in finding atomic arrangementsA Gaussian process using gradients and a squared exponential kernel over an atomic fingerprint was fitted to the energies and forces of a small set of random configurations.materials-chemistryA learning algorithm ran a synchrotron beamline to find a phase-change materialEarlier spectra were reduced to similarity weights supplying a prior for phase mapping, while each cycle's diffraction patterns were segmented into phase regions under physical constraints.materials-chemistryMachine-learned force model simulates silicon-oxygen structures from glass surfaces to monoxide grainsFitted interatomic potentials drove simulations, and structures that went beyond where the fit was supported were labelled with quantum calculations and added to the database.

Limits

The predictions are only as good as the description fed in: two materials that look alike in the chosen numbers but behave differently cannot be told apart. The uncertainty is itself a modelling assumption, so it can be quietly wrong, and confident nonsense far from the training data is a standing risk. Fitting cost grows quickly with the number of points, which limits how large a dataset can be used directly. And the underlying quantum calculations the model learns from carry their own approximations, which it reproduces rather than corrects.

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