© 2020

Machine Learning Meets Quantum Physics

  • Kristof T. Schütt
  • Stefan Chmiela
  • O. Anatole von Lilienfeld
  • Alexandre Tkatchenko
  • Koji Tsuda
  • Klaus-Robert Müller

Part of the Lecture Notes in Physics book series (LNP, volume 968)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Kristof T. Schütt, Stefan Chmiela, O. Anatole von Lilienfeld, Alexandre Tkatchenko, Koji Tsuda, Klaus-Robert Müller
    Pages 1-4
  3. Fundamentals

    1. Front Matter
      Pages 5-6
    2. Jan Hermann
      Pages 7-24
    3. Wiktor Pronobis, Klaus-Robert Müller
      Pages 25-36
    4. Grégoire Montavon
      Pages 37-62
  4. Incorporating Prior Knowledge: Invariances, Symmetries, Conservation Laws

    1. Front Matter
      Pages 63-65
    2. Aldo Glielmo, Claudio Zeni, Ádám Fekete, Alessandro De Vita
      Pages 67-98
    3. Gábor Csányi, Michael J. Willatt, Michele Ceriotti
      Pages 99-127
    4. Stefan Chmiela, Huziel E. Sauceda, Alexandre Tkatchenko, Klaus-Robert Müller
      Pages 129-154
    5. Felix Andreas Faber, Anders S. Christensen, O. Anatole von Lilienfeld
      Pages 155-169
  5. Deep Learning of Atomistic Representations

    1. Front Matter
      Pages 195-197
    2. Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, George E. Dahl
      Pages 199-214
    3. Kristof T. Schütt, Alexandre Tkatchenko, Klaus-Robert Müller
      Pages 215-230
  6. Atomistic Simulations

    1. Front Matter
      Pages 231-232
    2. Michael Gastegger, Philipp Marquetand
      Pages 233-252
    3. Matti Hellström, Jörg Behler
      Pages 253-275
    4. Huziel E. Sauceda, Stefan Chmiela, Igor Poltavsky, Klaus-Robert Müller, Alexandre Tkatchenko
      Pages 277-307
    5. Alexander Shapeev, Konstantin Gubaev, Evgenii Tsymbalov, Evgeny Podryabinkin
      Pages 309-329

About this book


Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume. 


To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials.


The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context. 


generative models kernel methods material modeling neural networks gaussian regression atomistic simulation polymer genome bayesian optimization quantum chemistry

Editors and affiliations

  • Kristof T. Schütt
    • 1
  • Stefan Chmiela
    • 2
  • O. Anatole von Lilienfeld
    • 3
  • Alexandre Tkatchenko
    • 4
  • Koji Tsuda
    • 5
  • Klaus-Robert Müller
    • 6
  1. 1.Machine LearningTechnical University of BerlinBerlinGermany
  2. 2.Machine Learning GroupTechnical University of BerlinBerlinGermany
  3. 3.Institute of Physical Chemistry and MARVELUniversity of BaselBaselSwitzerland
  4. 4.Department of Physics and Materials ScienceUniversity of LuxembourgLuxembourgLuxembourg
  5. 5.Graduate School of Frontier SciencesUniversity of TokyoKashiwaJapan
  6. 6.Computer ScienceTechnical University of BerlinBerlinGermany

About the editors

Kristof T. Schütt studied computer science at the Technische Universität Berlin where he received the MSc. in 2012 and the Ph.D. degree in 2018.

During his doctoral studies in the machine learning group of TU Berlin and at the Berlin Big Data Center, his research interests has been representation learning of atomistic systems, in particular the development of interpretable neural networks for applications in quantum chemistry.

Dr. Schütt has continued this research in a postdoctoral position at the Berlin Center for Machine Learning.

Stefan Chmiela is a postdoc researcher in the Machine Learning group at Technische Universität Berlin, where he obtained his Doctor degree in computer science in 2019.

His inter-disciplinary research revolves around developing efficient machine learning methods to approximate the many-body problem, without unraveling its full combinatorial complexity. A particular focus lies on the description of atomic interactions in quantum chemistry, under consideration of the natural invariants that restrict a system’s degrees of freedom.

O. Anatole von Lilienfeld is Associate Professor of Physical Chemistry at the University of Basel. Research in his laboratory deals with the development of improved methods for first principles based sampling of chemical compound space using quantum mechanics, super computers, Big Data, and machine learning.

Previously, he was an associate professor at the Free University of Brussels. From 2013 to 2015 he was a Swiss National Science Foundation professor at the University of Basel. He worked for Argonne and Sandia National Laboratories, and from 2007 to 2010 he was a distinguished Harry S. Truman Fellow at Sandia National Laboratories, after postdoctoral work at New York University and at the University of California Los Angeles. In 2005, he was awarded a PhD in computational chemistry from EPF Lausanne. His diploma thesis work was done at ETH Zürich and the University of Cambridge. He studied chemistry at ETH Zürich, the Ecole de Chimie Polymers et Materiaux in Strasbourg, and the University of Leipzig.

He is editor in chief of the IOP journal "Machine Learning: Science and Technology", has been awarded the Feynman Prize in Nanotechnology, and is an ERC consolidator grantee.

Alexandre Tkatchenko is a Professor of Theoretical Chemical Physics at the University of Luxembourg and Visiting Professor at the Berlin Big Data Center. He obtained his bachelor degree in Computer Science and a Ph.D. in Physical Chemistry at the Universidad Autonoma Metropolitana in Mexico City.

Between 2008 and 2010, he was an Alexander von Humboldt Fellow at the Fritz Haber Institute of the Max Planck Society in Berlin.

Between 2011 and 2016, he led an independent research group at the same institute.

Tkatchenko has given more than 230 plenary/keynote/invited talks, seminars and colloquia worldwide, published more than 150 articles in peer-reviewed academic journals (h-index=57), and serves on the editorial boards of Physical Review Letters (APS) and Science Advances (AAAS).

He received a number of awards, including elected Fellow of the American Physical Society, the Gerhard Ertl Young Investigator Award of the German Physical Society, and two flagship grants from the European Research Council (ERC): a Starting Grant in 2011 and a Consolidator Grant in 2017.

His group pushes the boundaries of quantum mechanics, statistical mechanics, and machine learning to develop efficient methods to enable accurate modeling and obtain new insights into complex materials.

Koji Tsuda received B.E., M.E., and Ph.D degrees from Kyoto University, Japan, in 1994, 1995, and 1998, respectively. Subsequently, he joined former Electrotechnical Laboratory (ETL), Tsukuba, Japan, as Research Scientist. When ETL was reorganized as AIST in 2001, he joined newly established Computational Biology Research Center, Tokyo, Japan.

In 2000–2001, he worked at GMD FIRST (currently Fraunhofer FIRST) in Berlin, Germany, as Visiting Scientist.

In 2003–2004 and 2006–2008, he worked at Max Planck Institute for Biological Cybernetics, Tübingen, Germany, first as Research Scientist and later as Project Leader.

Currently, he is Professor at Department of Computational Biology and Medical Sciences, Graduate School of Frontier Sciences, the University of Tokyo. He is also affiliated with National Institute of Material Science (NIMS) and RIKEN Center for Advanced Intelligence Project.

His current research interests include machine learning, computational biology and materials informatics.

Klaus-Robert Müller studied physics in Karlsruhe, Germany, from 1984 to 1989, and received the Ph.D. degree in computer science from Technische Universität Karlsruhe, Karlsruhe, in 1992. After completing a postdoctoral position at GMD FIRST, Berlin, Germany, he was a Research Fellow with The University of Tokyo, Tokyo, Japan, from 1994 to 1995. In 1995, he founded the Intelligent Data Analysis Group, GMD-FIRST (later Fraunhofer FIRST), and directed it until 2008. From 1999 to 2006, he was a Professor with the University of Potsdam, Potsdam Germany. He has been a Professor of computer science with Technische Universität Berlin, Berlin, since 2006; at the same time, he is co-directing the Berlin Big Data Center and directing the Berlin Center for Machine Learning.

His current research interests include intelligent data analysis, machine learning, deep learning, and machine learning for the sciences (brain–computer interfaces, quantum chemistry, cancer).

Dr. Müller was a recipient of the 1999 Olympus Prize by the German Pattern Recognition Society, DAGM, and he received the SEL Alcatel Communication Award in 2006, the Science Prize of Berlin awarded by the Governing Mayor of Berlin in 2014, and the Vodafone Innovation Award in 2017.

In 2012, he was elected as a member of the German National Academy of Sciences Leopoldina, and in 2017, a member of the Berlin Brandenburg Academy of sciences, and an External Scientific Member of the Max Planck Society.

He has published numerous papers and holds several patents (GS > 67000, h-index = 112).

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