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Quantum Machine Learning
Or
BAnatole von LilienfeldInstitute of Physical Chemistry and
National Center for Computational Design and Discovery of Novel
Materials (MARVEL), Department of Chemistry, University of Basel,
Switzerland
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Chang, OAvL, CHIMIA (2014)
correlations (inductive) vs. law (deductive)
Rupp, Tkatchenko, Muller, von Lilienfeld, Phys Rev Lett
(2012)
Erwin
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Chang, OAvL, CHIMIA (2014)
correlations (inductive) vs. law (deductive)
Rupp, Tkatchenko, Muller, von Lilienfeld, Phys Rev Lett
(2012)
Erwin
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( )
Kernel Ridge Regression
Solution
Kernel
e.g.
Regression
Rupp, Tkatchenko, Muller, von Lilienfeld, Phys Rev Lett
(2012)
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Hansen et al, J Phys Chem Lett (2015)Rupp et al, Phys Rev Lett
(2012)
Coulomb matrix (CM) Bag of Bonds (BoB)Molecule
● Unique but overcomplete● Invariances (Tra&Rot)● Compact●
Physical meaning● Fast● Simple metrics are not
smooth if sorted
● Not unique (homometricity)● Invariant (Tra&Rot)● Compact●
Physical meaning● Fast● Simple metrics are smooth
Representation
Rupp, Tkatchenko, Muller, von Lilienfeld, Phys Rev Lett (2012);
Hansen et al, J Phys Chem Lett (2015)
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The bigger the data the better …
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Error ~ a/Nb
→ log(Error) = log(a) - blog(N)
Cortes, C., Jackel, L. D., Solla, S. A., Vapnik, V., &
Denker, J. S. (1994). Learning curves: Asymptotic values and rate
of convergence.Advances in Neural Information Processing Systems,
6, 327-334
Müller, K.-R. et al, Neural Comput (1996)
The bigger the data the better …
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Cortes, C., Jackel, L. D., Solla, S. A., Vapnik, V., &
Denker, J. S. (1994). Learning curves: Asymptotic values and rate
of convergence.Advances in Neural Information Processing Systems,
6, 327-334
Müller, K.-R. et al, Neural Comput (1996)
Error ~ a/(N’)b , e.g. N’ = N c
→ log(Error) = log(a) - b c - b log(N)
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Error ~ a/Nb
→ log(Error) = log(a) - blog(N)
K ~ Ψα ~ Ô
Ramakrishnan, OAvL, CHIMIA (2015)
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Error ~ a/Nb
→ log(Error) = log(a) - blog(N) Ramakrishnan, OAvL, CHIMIA
(2015)
K ~ Ψα ~ Ô
Ramakrishnan, OAvL, CHIMIA (2015)
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Crystals
Faber et al, Phys Rev Lett (2016) arxiv.org/abs/1508.05315
● most abundant quaternary crystal structure in Inorganic
Crystal Structure Database
● can emit light when exposed to ionic radiation (→ Scintillator
candidates)
● transparent, glossy, colorless and soft crystal in Fm3m space
group
● AlNaK2F
6 found in Rocky Mountains, Virginia, or the Apennines
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Crystals
Faber et al, Phys Rev Lett (2016) arxiv.org/abs/1508.05315
Reduction in cost:DFT: ~20 M CPU hML: ~20 CPU h
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Ramakrishnan et al, Scientific Data (2014)
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Ramakrishnan et al, Scientific Data (2014)
``Enumeration surpasses imagination’’J.-L. Reymond
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"Prediction errors of molecular machine learning models lower
than hybrid DFT errors", F. A. Faber, L. Hutchison, B. Huang, J.
Gilmer, S. S. Schoenholz, G. E. Dahl, O. Vinyals, S. Kearnes, P. F.
Riley, OAvL J Chem Theory Comput (2017)
arxiv.org/abs/1702.05532
https://arxiv.org/abs/1702.05532
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"Prediction errors of molecular machine learning models lower
than hybrid DFT errors", F. A. Faber, L. Hutchison, B. Huang, J.
Gilmer, S. S. Schoenholz, G. E. Dahl, O. Vinyals, S. Kearnes, P. F.
Riley, OAvL J Chem Theory Comput (2017)
arxiv.org/abs/1702.05532
https://arxiv.org/abs/1702.05532
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"Prediction errors of molecular machine learning models lower
than hybrid DFT errors", F. A. Faber, L. Hutchison, B. Huang, J.
Gilmer, S. S. Schoenholz, G. E. Dahl, O. Vinyals, S. Kearnes, P. F.
Riley, OAvL J Chem Theory Comput (2017)
arxiv.org/abs/1702.05532
https://arxiv.org/abs/1702.05532
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Representation
Huang, OAvL, J Chem Phys Comm (2016)
arxiv.org/abs/1608.06194
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Huang, OAvL, J Chem Phys Comm (2016)
arxiv.org/abs/1608.06194
Representation
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Huang, OAvL, J Chem Phys Comm (2016)
arxiv.org/abs/1608.06194
BAML
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Huang, OAvL, J Chem Phys Comm (2016)
arxiv.org/abs/1608.06194
6k constitutional isomers of C7O
2H
10
BAML
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Huang, OAvL, J Chem Phys Comm (2016)
arxiv.org/abs/1608.06194
6k constitutional isomers of C7O
2H
10
QM9 (134k molecules)
BAML
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Huang, OAvL, J Chem Phys Comm (2016)
arxiv.org/abs/1608.06194
BAML
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Faber et al, in prep (2017)
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Faber et al, in prep (2017)
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Faber et al, in prep (2017)
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Faber et al, in prep (2017)
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Faber et al, in prep (2017)
Faber et al, Phys Rev Lett (2016) arxiv.org/abs/1508.05315
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Atoms + London + Axilrod-Teller-Muto (LATM)
QM7b C7O2H10 QM9
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
an atom in a molecule: “AM-on”
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
an atom in a molecule: “AM-on”
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146 Huang,
von Lilienfeld, https://arxiv.org/abs/1707.04146
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146 Huang,
von Lilienfeld, https://arxiv.org/abs/1707.04146
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146 Huang,
von Lilienfeld, https://arxiv.org/abs/1707.04146
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146 Huang,
von Lilienfeld, https://arxiv.org/abs/1707.04146
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
http://www.youtube.com/watch?v=vaDnvmJvcfo
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Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
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Initial Converged
Outlook
Christensen et al, in prep (2017)
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"Genetic optimization of training sets for improved machine
learning models of molecular properties", N. J. Browning, R.
Ramakrishnan, OAvL, U. Rothlisberger J. Phys. Chem. Lett (2017)
http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.7b00038http://arxiv.org/abs/1611.07435
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"Genetic optimization of training sets for improved machine
learning models of molecular properties", N. J. Browning, R.
Ramakrishnan, OAvL, U. Rothlisberger J. Phys. Chem. Lett (2017)
http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.7b00038http://arxiv.org/abs/1611.07435
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"Genetic optimization of training sets for improved machine
learning models of molecular properties", N. J. Browning, R.
Ramakrishnan, OAvL, U. Rothlisberger J. Phys. Chem. Lett (2017)
http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.7b00038http://arxiv.org/abs/1611.07435
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"Genetic optimization of training sets for improved machine
learning models of molecular properties", N. J. Browning, R.
Ramakrishnan, OAvL, U. Rothlisberger J. Phys. Chem. Lett (2017)
http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.7b00038http://arxiv.org/abs/1611.07435
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"Genetic optimization of training sets for improved machine
learning models of molecular properties", N. J. Browning, R.
Ramakrishnan, OAvL, U. Rothlisberger J. Phys. Chem. Lett (2017)
http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.7b00038http://arxiv.org/abs/1611.07435
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"Genetic optimization of training sets for improved machine
learning models of molecular properties", N. J. Browning, R.
Ramakrishnan, OAvL, U. Rothlisberger J. Phys. Chem. Lett (2017)
http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.7b00038http://arxiv.org/abs/1611.07435
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Δ-ML
Ramakrishnan et al, J Chem Theory Comput (2015)
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Ramakrishnan et al, J Chem Theory Comput (2015)
CCSD(T)G4MP2Δ-ML
6k constitutional isomers of C7O
2H
10
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Ramakrishnan et al, J Chem Theory Comput (2015)
Ranking 10k diastereomers derived from 6k constitutional isomers
of C7O
2H
10→ Global minimum, and its 10 closest isomers …
Δ-ML
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R Ramakrishnan et al JCTC (2015)
CCSD(T)G4MP2
Δ-ML
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PM7 1k 10k86 → 74 → 58 kcal/mol
R Ramakrishnan et al JCTC (2015)
Δ-ML
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ML
R Ramakrishnan et al JCTC (2015)
Δ-ML
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Conclusions1. Instantaneous QM quality predictions
2. Learning curves reveal quality of ML model
3. Select studiesa. Understanding the role of representations:
JCP (2016)b. Baseline: Δ-ML: JCTC (2015)c. ML exceeds DFT accuracy:
arxiv (2017)d. Training set composition: JPCL (2017)e. Crystals:
PRL (2016)
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Inductive (Data)1. Assume a law2. Metric3. Examples4. Infer5.
New combination
Fast (ms)Arbitrary reference Automatic improvement
Transferable?Minimally condensed
Deductive (Laws)1. Assume a law2. Approximate3. Solve4.
Predict5. New regimes
Slow (depending on approx.)Approximation dependentHuman
improvement
Transferable?Maximally condensed
Conclusions IIScientific method - proper way to gain
knowledge
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http://www.youtube.com/watch?v=S6r6yWuKs7g
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Rupp et al, J Phys Chem Lett (2015)
NMR shifts of ~850 k Carbon atoms in 134 k organic molecules at
negligible cost
Atoms
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Rupp et al, J Phys Chem Lett (2015)
http://www.youtube.com/watch?v=ZQ3KtucI97o
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Rupp et al, J Phys Chem Lett (2015)
=
Atoms
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Rupp et al, J Phys Chem Lett (2015)
Atoms
![Rupp Clary[1]](https://img.dokumen.tips/doc/110x75/545988f8af795998788b578b/rupp-clary1.jpg)
