Volume VII — Data and Descriptors#
The methods of the earlier volumes each compute a property from a structure directly: solve for the electrons, integrate the equations of motion, sum the hills. Machine learning proposes instead to fit that map from examples — which changes the central question from how to compute the property to how to present the structure.
These three notebooks restore Lectures 10 and 11, which the original exercise set announced but never delivered. The first builds a descriptor: a representation of an atomic environment that is invariant to translation, rotation and relabelling by construction, and whose blind spots can be established by proof rather than discovered later in a model that quietly cannot represent what it was asked to. The second takes those descriptors as data and asks the questions that follow — how to project a high-dimensional set of environments down to something a person can look at, and how to choose a small, representative subset of a large ensemble to compute expensively. The third closes the loop and fits a potential: a curated dataset, kernel ridge regression by exact linear algebra, the learning curve that prices every training label, and a precise measurement of where the fitted model fails silently — and of the one cheap number that flags the failure before it is used.
Unlike the rest of this course these notebooks use no committed calculation. Every structure is built from its lattice definition, so every number can be re-derived from scratch.
Source lectures
This volume develops Lectures 10 and 11 of Molecular and Materials
Modelling (FS 2023) — machine learning for atomistic systems and
dimensionality reduction and sampling — as new exercises designed by the
author, the original exercise set having announced these lectures without
delivering them. Each notebook repeats its provenance in its overview; the full
lecture map is in manifest.yml.