Quantum Mechanics, Chemical Space, And Machine Learning Or

Transcription

1 Quantum Mechanics, Chemical Space, And Machine Learning Or B Anatole von Lilienfeld Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, Switzerland Many of the most relevant chemical properties of matter depend explicitly on atomistic details, rendering a first principles approach mandatory. Alas, even when using high-performance computers, brute force high-throughput screening of compounds is beyond any capacity for all but the simplest systems and properties due to the combinatorial nature of chemical space, i.e. all compositional, constitutional, and conformational isomers. Consequently, efficient exploration algorithms need to exploit all implicit redundancies present in chemical space. I will discuss recently developed statistical learning approaches for interpolating quantum mechanical observables in compositional and constitutional space.

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3 How do we do physics? 1. Guess a law 2. If it doesn t compare to experiment it s wrong Feynman

4 Theory to understand chemistry to help design experiments predictions that can be falsified 1. when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind. Lord Kelvin 2. we understand a molecule when we can predict its properties with a degree of accuracy considered quantitative. M. Quack, ETHZ (2000) 3. It is nice to know that the computer understands the problem. But I would like to understand it too. E. Wigner compare to experiment (arbiter)

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6 Configuration + Composition Chemical Space Young-Tae Chang et al C&E News 93 (12) (2015)

7 correlations (inductive) supervised learning Chang, OAvL, CHIMIA (2014)

8 Configuration + Composition Chemical Space Young-Tae Chang et al C&E News 93 (12) (2015)

9 How many are possible?

10 ``The greatest shortcoming of the human race is our inability to understand the exponential function Al Bartlett, U of Colorado Boulder J.-L. Reymond and coworkers, J Am Chem Soc (2009) and ff

11 ``The greatest shortcoming of the human race is our inability to understand the exponential function Al Bartlett, U of Colorado Boulder J.-L. Reymond and coworkers, J Am Chem Soc (2009) and ff

12 Conclusions 1. Instantaneous QM quality predictions 2. Learning curves reveal quality of ML model 3. Rate and offset depend on a. Baseline: Δ-ML (prior expert knowledge about property) b. Representation: Uniqueness and energy (property independent) c. Domain of applicability: Data (properties and structures)

13 Kernel Ridge Regression Kernel e.g. Regression ( Solution )

14 Virshup, Yang, Beratan et al J Am Chem Soc (2013)

15 Virshup, Yang, Beratan et al J Am Chem Soc (2013)

16 From molecule to Coulomb matrix (CM) to Bag of Bonds (BOB) Molecule Coulomb matrix (CM) Rupp et al, Phys Rev Lett (2012) Unique but overcomplete Invariances (Tra&Rot) Compact Physical meaning Fast Simple metrics are not smooth if sorted Bag of Bonds (BoB) Hansen et al, J Phys Chem Lett (2015) Not unique (homometricity) Invariant (Tra&Rot) Compact Physical meaning Fast Simple metrics are smooth

17 Big Data N Train Model(N)

18 Big Data N Rupp et al, Phys Rev Lett (2012) Train QM: ~1000 seconds ML: ~milli seconds Query Model(N) Predict

19 "Machine learning for many-body physics: efficient solution of dynamical mean-field theory", L.-F. Arsenault, OAvL, A. J. Millis, submitted, arxiv.org/abs/ "Constant Size Molecular Descriptors For Use With Machine Learning", C. R. Collins, G. J. Gordon, OAvL, D. J. Yaron, submitted to J. Chem. Inf. Model. "Machine Learning, Quantum Mechanics, and Chemical Compound Space" R. Ramakrishnan, OAvL (in press) Reviews in Computational Chemistry, arxiv.org/abs/ "Understanding molecular representations in machine learning: The role of uniqueness and target similarity", B. Huang, OAvL, accepted J. Chem. Phys. (2016), arxiv.org/abs/ "Machine Learning Energies of 2 M Elpasolite (ABC2D6) Crystals", F. Faber, A. Lindmaa, OAvL, R. Armiento, Phys. Rev. Lett (2016) arxiv.org/abs/ "Electronic Spectra from TDDFT and Machine Learning in Chemical Space", R. Ramakrishnan, M. Hartmann, E. Tapavicza, OAvL, J. Chem. Phys (2015) arxiv.org/abs/ "Machine Learning for Quantum Mechanical Properties of Atoms in Molecules", M. Rupp, R. Ramakrishnan, OAvL, J. Phys. Chem. Lett (2015). arxiv.org/abs/ "Machine Learning Predictions of Molecular Properties: Accurate Many-Body Potentials and Non-Locality in Chemical Space", K. Hansen, F. Biegler, R. Ramakrishnan, W. Pronobis, OAvL, K.-R. Mueller, A. Tkatchenko, J. Phys. Chem. Lett (2015). "Transferable atomic multipole machine learning models for small organic molecules", T. Bereau, D. Andrienko, OAvL, J. Chem. Theory Comput (2015) arxiv.org/abs/ "Machine Learning of Parameters for Accurate Semiempirical Quantum Chemical Calculations", P. Dral, OAvL, W. Thiel, J. Chem. Theory Comput (2015) "Big Data meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach", R. Ramakrishnan, P. O. Dral, M. Rupp, OAvL, J. Chem. Theory Comput (2015), arxiv.org/abs/ "Crystal Structure Representations for Machine Learning Models of Formation Energies", F. Faber, A. Lindmaa, OAvL, R. Armiento, Int. J. Quantum Chem. doi: /qua (2015), arxiv.org/abs/ "Many Molecular Properties from One Kernel in Chemical Space", R. Ramakrishnan, OAvL, CHIMIA (2015) ; arxiv.org/abs/ "Fourier series of atomic radial distribution functions: A molecular fingerprint for machine learning models of quantum chemical properties", OAvL, R. Ramakrishnan, M. Rupp, A. Knoll, Int. J. Quantum Chem. doi: /qua.2491 (2015) arxiv.org/abs/ "Machine learning for Many-Body Physics : The case of the Anderson impurity model", L.-F. Arsenault, A. Lopez-Bezanilla, OAvL, A. Millis, Phys. Rev. B (2014) arxiv.org/abs/ "Quantum chemistry structures and properties of 134 kilo molecules", R. Ramakrishnan, P. O. Dral, M. Rupp, OAvL, Scientific Data (2014) "Modeling electronic quantum transport with machine learning", A. Lopez-Bezanilla, OAvL, Phys Rev B (2014), arxiv.org/abs/ "Assessment and validation of machine learning methods for predicting molecular atomization energies", K. Hansen, G. Montavon, F. Biegler, S. Fazli, M. Rupp, M. Scheffler, OAvL, A. Tkatchenko, K-R. Mueller J Chem Theory Comput (2013) "Machine Learning of Molecular Electronic Properties in Chemical Compound Space", G. Montavon, M. Rupp, V. Gobre, A. Vazquez-Mayagoitia, K. Hansen, A. Tkatchenko, K-R. Mueller, OAvL, New J. Phys (2013) arxiv.org/abs/ "Learning Invariant Representations of Molecules for Atomization Energy Prediction", G. Montavon, K. Hansen, S. Fazli, M. Rupp, F. Biegler, A. Ziehe, A. Tkatchenko, OAvL, K.-R. Mueller, Advances in Neural Information Processing Systems (2012) "Fast and accurate modeling of molecular atomization energies with machine learning", M. Rupp, A. Tkatchenko, K.-R. Mueller, OAvL Phys. Rev. Lett (2012) arxiv.org/abs/ e "Towards quantitative structure-property relationships for charge transfer rates of polycyclic aromatic hydrocarbons" M. Misra, D. Andrienko, B. Baumeier, J.-L. Faulon, OAvL J. Chem. Theory Comput (2011) Navigating Chemical Compound Space, IPAM, UCLA

20 Conclusions 1. Instantaneous QM quality predictions 2. Learning curves reveal quality of ML model 3. Rate and offset depend on a. Baseline: Δ-ML (prior expert knowledge about property) b. Representation: Uniqueness and energy (property independent) c. Domain of applicability: Data (properties and structures)

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22 The bigger the data the better Error ~ a/nb K.-R. Mueller et al, Neural Comput (1996) log(error) = a - blog(n)

23 Ramakrishnan et al, Scientific Data (2014) ``Enumeration surpasses imagination J.-L. Reymond Reymond, Acc Chem Res (2015) 6k constitutional isomers of C7O2H10

24 Error ~ a/nb K.-R. Mueller et al, Neural Comput (1996) log(error) = a - blog(n) Ramakrishnan, OAvL, CHIMIA (2015)

25 Error ~ a/nb K.-R. Mueller et al, Neural Comput (1996) log(error) = a - blog(n) K~Ψ α~ô Ramakrishnan, OAvL, CHIMIA (2015)

26 Error ~ a/(n )b, e.g. N = N/3 K.-R. Mueller et al, Neural Comput (1996) log(error) = a + 3b - b log(n) Ramakrishnan, OAvL, CHIMIA (2015)

27 Conclusions 1. Instantaneous QM quality predictions 2. Learning curves reveal quality of ML model 3. Rate and offset depend on a. Baseline: Δ-ML (prior expert knowledge about property) b. Representation: Uniqueness and energy (property independent) c. Domain of applicability: Data (properties and structures)

28 Δ-ML Ramakrishnan et al, J Chem Theory Comput (2015)

29 Δ-ML 6k constitutional isomers of C7O2H10 Ramakrishnan et al, J Chem Theory Comput (2015) G4MP2 CCSD(T)

30 Δ-ML Ranking 10k diastereomers derived from 6k constitutional isomers of C 7O2H10 Global minimum, and its 10 closest isomers Ramakrishnan et al, J Chem Theory Comput (2015)

31 Δ-ML G4MP2 R Ramakrishnan et al JCTC (2015) CCSD(T)

32 Δ-ML PM7 86 R Ramakrishnan et al JCTC (2015) 1k 74 10k 58 kcal/mol

33 Δ-ML ML R Ramakrishnan et al JCTC (2015)

34 Conclusions 1. Instantaneous QM quality predictions 2. Learning curves reveal quality of ML model 3. Rate and offset depend on a. Baseline: Δ-ML (prior expert knowledge about property) b. Representation: Uniqueness and energy (property independent) c. Domain of applicability: Data (properties and structures)

35 Representation Huang, OAvL, accepted in J Chem Phys Comm (2016) arxiv.org/abs/

36 Representation OAvL et al, IJQC (2013) Huang, OAvL, accepted in J Chem Phys Comm (2016) arxiv.org/abs/

37 Representation Huang, OAvL, accepted in J Chem Phys Comm (2016) arxiv.org/abs/

38 Representation Huang, OAvL, accepted in J Chem Phys Comm (2016) arxiv.org/abs/

39 Representation 6k constitutional isomers of C7O2H10 Huang, OAvL, accepted in J Chem Phys Comm (2016) arxiv.org/abs/

40 Representation 6k constitutional isomers of C7O2H10 QM9 (134k molecules) Huang, OAvL, accepted in J Chem Phys Comm (2016) arxiv.org/abs/

41 Representation Huang, OAvL, accepted in J Chem Phys Comm (2016) arxiv.org/abs/

42 Conclusions 1. ML makes instantaneous QM quality predictions 2. Learning curves reveal quality of ML model 3. Rate and offset depend on a. Uniqueness and target similarity (model dependent) b. Properties and structures (data dependent) c. Baseline (expert dependent)

43 Crystals Elpasolite (K2NaAlF6-symmetry) is a vitreous, transparent, luster, colorless and soft quaternary crystal in the Fm3m space group which can be found in the Rocky Mountains, Virginia, or the Apennines. It is the most abundant quaternary crystal present in the Inorganic Crystal Structure Database. Some Elpasolites emit light when exposed to ionic radiation. This makes them interesting material candidates for scintillator devices. Faber et al, Phys Rev Lett (2016) arxiv.org/abs/

44 Crystals Elpasolite (K2NaAlF6-symmetry) is a vitreous, transparent, luster, colorless and soft quaternary crystal in the Fm3m space group which can be found in the Rocky Mountains, Virginia, or the Apennines. It is the most abundant quaternary crystal present in the Inorganic Crystal Structure Database. Some Elpasolites emit light when exposed to ionic radiation. This makes them interesting material candidates for scintillator devices. Reduction in cost: DFT: ~20 M CPU hours (optimized) ML: ~20 CPU hours (not optimized) Faber et al, Phys Rev Lett (2016) arxiv.org/abs/

45 Crystals Faber et al, Phys Rev Lett (2016) arxiv.org/abs/

46 Crystals Faber et al, Phys Rev Lett (2016) arxiv.org/abs/

47 Crystals Faber et al, Phys Rev Lett (2016) arxiv.org/abs/

48 Crystals Faber et al, Phys Rev Lett (2016) arxiv.org/abs/

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50 Conclusions 1. ML makes instantaneous QM quality predictions 2. Learning curves reveal quality of ML model 3. Rate and offset depend on a. Uniqueness and target similarity (model dependent) b. Properties and structures (data dependent) c. Baseline (expert dependent)

51 Conclusions II Scientific method - how to gain knowledge Inductive 1. Assume a law 2. Metric 3. Examples 4. Infer 5. New combination Deductive 1. Assume a law 2. Approximate 3. Solve 4. Predict 5. New regimes Fast (ms) Arbitrary reference Automatic improvement Slow (depending on approx.) Approximation dependent Human improvement Transferable? Minimally condensed Transferable? Maximally condensed