Chapter on Machine Learning in Quantum Chemistry in a Tutorial Way

My book chapter shows in a tutorial way how to use machine learning to assist quantum chemistry research.

The chapter – available for free download till November 6 – is a part of the book edited by Kenneth Ruud and Erkki J. Brändas. It collects a dozen of contributions to the 10th Triennial Congress of the International Society for Theoretical Chemical Physics (ISTCP-X). This was a huge congress with 500+ participants. It was held in pre-COVID-19 times in Tromsø, Norway, where the sun never set below the horizon at that time of the year. The team of the organizers led by Kenneth Ruud did really amazing job to bring together forefront science in chemical physics. We with Alan Aspuru-Guzik had a pleasure and honor to organize a session on Machine Learning and Data-Driven Approaches in Chemical Physics. This was also my last conference in Europe – who knows when I will be able to attend next meeting there?

Since then I have joined Xiamen University. I quickly was posed with a question: how to teach undergraduates the brief introduction to machine learning in quantum chemistry in an easily comprehensible way? I also wanted to give the students hands-on experience with ML. This shaped my approach to writing the chapter. Instead of giving dry account of published research, the chapter goes from simple to more advanced examples, all of which could be simulated on a computer by students.

It starts with describing general aspects of ML, gives simple mathematical description of a specific algorithm – kernel ridge regression. First simulation examples highlight pitfalls of ML such as overfitting and underfitting, whose origins explained based on simple mathematical considerations, and shows how these problems can be avoided. It follows by demonstrating the power of Δ-ML and discusses semiempirical parameter learning. Later it shows how to describe molecular potential energy surfaces with spectroscopic accuracy using ML and structure-based sampling – the students can reproduce published numbers. The chapter concludes with discussing aspects of ML applied to nonadiabatic excited-state dynamics, demonstrating for example that inclusion of critical points into the training set allows to describe even very narrow nonadiabatic couplings.

Detailed instructions on how to perform ML calculations for each example are given in an online tutorial. For this, I also prepared MLatom 1.1 release.

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