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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
Chang, OAvL, CHIMIA (2014)
correlations (inductive) vs. law (deductive)
Rupp, Tkatchenko, Muller, von Lilienfeld, Phys Rev Lett (2012)
Erwin
Chang, OAvL, CHIMIA (2014)
correlations (inductive) vs. law (deductive)
Rupp, Tkatchenko, Muller, von Lilienfeld, Phys Rev Lett (2012)
Erwin
( )
Kernel Ridge Regression
Solution
Kernel
e.g.
Regression
Rupp, Tkatchenko, Muller, von Lilienfeld, Phys Rev Lett (2012)
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)
The bigger the data the better …
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 …
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)
Error ~ a/Nb
→ log(Error) = log(a) - blog(N)
K ~ Ψα ~ Ô
Ramakrishnan, OAvL, CHIMIA (2015)
Error ~ a/Nb
→ log(Error) = log(a) - blog(N) Ramakrishnan, OAvL, CHIMIA (2015)
K ~ Ψα ~ Ô
Ramakrishnan, OAvL, CHIMIA (2015)
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
Crystals
Faber et al, Phys Rev Lett (2016) arxiv.org/abs/1508.05315
Reduction in cost:DFT: ~20 M CPU hML: ~20 CPU h
Ramakrishnan et al, Scientific Data (2014)
Ramakrishnan et al, Scientific Data (2014)
``Enumeration surpasses imagination’’J.-L. Reymond
"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
"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
"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
Representation
Huang, OAvL, J Chem Phys Comm (2016) arxiv.org/abs/1608.06194
Huang, OAvL, J Chem Phys Comm (2016) arxiv.org/abs/1608.06194
Representation
Huang, OAvL, J Chem Phys Comm (2016) arxiv.org/abs/1608.06194
BAML
Huang, OAvL, J Chem Phys Comm (2016) arxiv.org/abs/1608.06194
6k constitutional isomers of C7O
2H
10
BAML
Huang, OAvL, J Chem Phys Comm (2016) arxiv.org/abs/1608.06194
6k constitutional isomers of C7O
2H
10
QM9 (134k molecules)
BAML
Huang, OAvL, J Chem Phys Comm (2016) arxiv.org/abs/1608.06194
BAML
Faber et al, in prep (2017)
Faber et al, in prep (2017)
Faber et al, in prep (2017)
Faber et al, in prep (2017)
Faber et al, in prep (2017)
Faber et al, Phys Rev Lett (2016) arxiv.org/abs/1508.05315
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Atoms + London + Axilrod-Teller-Muto (LATM)
QM7b C7O2H10 QM9
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
an atom in a molecule: “AM-on”
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
an atom in a molecule: “AM-on”
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146 Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146 Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146 Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146 Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
http://www.youtube.com/watch?v=vaDnvmJvcfo
Huang, von Lilienfeld, https://arxiv.org/abs/1707.04146
Initial Converged
Outlook
Christensen et al, in prep (2017)
"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
"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
"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
"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
"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
"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
Δ-ML
Ramakrishnan et al, J Chem Theory Comput (2015)
Ramakrishnan et al, J Chem Theory Comput (2015)
CCSD(T)G4MP2Δ-ML
6k constitutional isomers of C7O
2H
10
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
R Ramakrishnan et al JCTC (2015)
CCSD(T)G4MP2
Δ-ML
PM7 1k 10k86 → 74 → 58 kcal/mol
R Ramakrishnan et al JCTC (2015)
Δ-ML
ML
R Ramakrishnan et al JCTC (2015)
Δ-ML
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)
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
http://www.youtube.com/watch?v=S6r6yWuKs7g
Rupp et al, J Phys Chem Lett (2015)
NMR shifts of ~850 k Carbon atoms in 134 k organic molecules at negligible cost
Atoms
Rupp et al, J Phys Chem Lett (2015)
http://www.youtube.com/watch?v=ZQ3KtucI97o
Rupp et al, J Phys Chem Lett (2015)
=
Atoms
Rupp et al, J Phys Chem Lett (2015)
Atoms
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