Fundamentals of Atomistic Machine Learning

This course is aimed at graduate students in physics, chemistry, or engineering, as well as researchers in related disciplines. It covers the most important aspects of atomistic machine learning, i.e., the application of machine learning tools to predict properties of atomistic systems (molecules or condensed matter). Emphasis is made on learning properties derived from ab initio electronic structure calculations, and in the application of these tools to perform and analyze atomistic simulations. The course is suitable for beginners in this field and attempts to cover basic aspects, moving all the way to cutting-edge topics.
The course is organized into 6 lectures (1.5 hours each) on the blackboard and 4 hands-on assignments using Jupyter Notebooks. The hands-on assignments can be completed as homework, and additional time will be allotted for answering questions.

Prerequisites
Knowledge of graduate-level quantum mechanics and statistical mechanics is recommended. Furthermore, basic understanding of molecular simulation and electronic-structure
calculations is useful. However, an effort will be made to make the content understandable for a broad audience.

Contents
Module 1 - Machine learning (ML) in the Natural Sciences: A change of paradigm. Why did the AI revolution happen? Artificial neural networks as a universal function approximator
and a tool to overcome the curse of dimensionality. Example applications in chemistry, materials science, biology, and condensed matter physics.
Module 2 - Basics of ML: Supervised and unsupervised learning. Common tasks such as regression and classification. Generative models. Loss function. Mini-batch gradient descent.
Deep neural networks, kernel regression, and other algorithms.
Module 3 - Atomistic ML: Representation of local and global physical quantities. Equivariance and invariance. Permutation, rotation, and translation symmetry.
Nearsightedness of matter. Concept of descriptors.
Module 4 - Descriptors: Behler-Parrinello descriptors. SOAP descriptors. DeePMD learned descriptors. Using descriptors for dimensional reduction and characterization of atomic
environments (fingerprints). Message passing graph neural networks.
Module 5 - ML models for interatomic interactions: Classical and ab initio molecular dynamics. Limitations of semi-empirical and ab initio models. Short-range machine learning
models for the interatomic interactions. System specific models. Active learning. Large atomic (foundation) models.
Module 6 - Long-range interactions: When and why are they needed? First principles electrostatics based on Wannier centers. Connection to modern theory of polarization. Other
formalisms for treating long-range interactions and problems with charge conservation.

Bibliography
Books
A. White, "Deep Learning for Molecules and Materials", Living Journal of Computational Molecular
Science, 3(1),1499 (2022).
Y. Bengio, I. Goodfellow, and A. Courville. "Deep Learning", MIT press (2017)
D. Marx and J. Hutter, "Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods".
Cambridge University Press (2009)
J. Kohanoff, "Electronic structure calculations for solids and molecules: theory and computational
methods". Cambridge university press (2006)
D. Vanderbilt, "Berry phases in electronic structure theory: electric polarization, orbital magnetization
and topological insulators". Cambridge University Press (2018)

Scientific articles
W. E. et al., "Machine-learning-assisted modeling", Physics Today 74 (7), 36–41 (2021)
G. Carleo et al., "Machine learning and the physical sciences", Rev. Mod. Phys. 91, 045002 (2019)
F. Musil et al., "Physics-Inspired Structural Representations for Molecules and Materials", Chem.
Rev. 121, 16, 9759–9815 (2021)
V. Deringer et al, "Machine learning interatomic potentials as emerging tools for materials science",
Advanced Materials 31, 46 (2019)
L. Zhang et al., "A deep potential model with long-range electrostatic interactions", J. Chem. Phys.
156, 124107 (2022)

Course shared documents