Discovery	  of	  Functional	  Molecules	  and	  Materials	  by	  Artificial	  Intelligence	  Techniques
津田 宏治
東京大学

Discovery	  of	  new	  functional	  molecules	  and	  materials	  is	  of	  national	  importance2

First	  Principles	  Calculations
Accurate,	  Slow

• Full	  configuration	  interaction• Wave	  function	  based	  • Density	  functional	  theory• Semi-­‐empirical• Empirical	  potentials
Inaccurate,	  Fast

Old	  Picture

Simulation(DFT	  etc)

Experiments

New	  Picture

Experimental	  Design

Artificial	  Intelligence

Simulation(DFT	  etc)
Features

Experiments

3	  Techniques	  and	  4	  Studies• Virtual	  Screening– Discovering	  low-­‐LTC	  compounds• Bayesian	  Optimization– Optimization	  of	  grain	  boundary	  – Design	  of	  Si-­‐Ge	  nanostructures• Monte	  Carlo	  Tree	  Search– Designing	  optimal	  RNA	  sequences

6Screening	  by	  first	  principles	  calculations	  alone
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Score	   Score Score	   Score	   Score	   Score	   Score	   Score	   Score Score	  123456
7
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910

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Virtual	  Screening
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Virtual	  Screening
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Score	   Score	   Score Pred.	   Pred.	   Pred.	   Pred.	   Pred.	   Pred.	   Pred.	  
123Score	  	   Score	   Score	  	   Score	  	   Score	  	   Score	  	   Score	  	  45678910Machine	  Learning

910

Thermoelectric materials

PowerLow  T
Electric current

Heat fluxp-­typen-­type

Electric current

Figure  of  Merit

Electric current(S2 s/k )THigh  T

S: Seebeck coefficients:	  electrical	  conductivityk:	  	  thermal	  conductivity

11

Discovering	  Compounds	  of	  	  Low	  Thermal	  Conductivity: Motivation• Isao	  Tanaka’s	  Lab	  developed	  a	  system	  capable	  of	  calculating	  lattice	  thermal	  conductivity	  (LTC)– First-­‐principles	  anharmonic lattice	  dynamics	  calculations– Solving	  Boltzmann	  transport	  equation	  with	  the	  single-­‐mode	  relaxation-­‐time	  approximation• Too	  slow	  for	  screening	  in	  a	  large	  database– One	  LTC	  can	  take	  one	  WEEK	  with	  hundreds	  of	  cores

Lattice thermal conductivity : calc. vs. exp.
Zincblende and Wurtzite types
300K;	  LBTE	  with	  phonon-­‐isotope	  effect1414

Discovering	  Compounds	  of	  	  Low	  Thermal	  Conductivity from	  Database(Seko et	  al.,	  PRL	  2015)• Compute	  LTC	  of	  101	  prototypical	  compounds– Rocksalt,	  Zincblende,	  Wurtzite-­‐type– Best	  LTC:	  0.9	  W/m・K	  • Predict	  LTC	  of	  54779	  compounds	  in	  Materials	  Project	  Database– Additional	  LTC	  calculations	  for	  best	  8	  compounds– Five	  had	  impressive	  LTC	  of	  <	  0.2	  	  W/m・K	  (@300K)

16

Bayesian	  Optimization(Jones	  et	  al.,	  1998)• Find	  best	  data	  points	  with	  minimum	  number	  of	  observations• Choose	  next	  point	  to	  observe	  to	  discover	  the	  best	  ones	  as	  early	  as	  possible

Bayesian	  Optimization	  (1)
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Bayesian	  Optimization	  (2)	  Mat.
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Predicted	  Scores
Score	   Score	   Score	   Pred. Pred. Pred. Pred. Pred. Pred. Pred.
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3Score Score Score Score Score Score Score
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8910Var.	  
4Var.
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Predicted	  Variances

Var.
9Var.
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Bayesian	  Optimization	  (3)
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Bayesian	  Optimization	  (4)
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1238Score Score Score Score Score Score
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910Var.	  
4Var.	  5Var.	  6Var.	  7Var.	  9Var.	  1021Where	  to	  observe	  next?
Current
Maximum

Measured	  Value
Explanatory	  Variable

22Gaussian	  Process
Current
Maximum

Measured	  Value
Explanatory	  Variable23

Maximum	  probability	  of	  improvement
Current
Maximum

Measured	  Value
Explanatory	  Variable

24Finding	  single	  and	  binary	  component	  solids	  with	  high	  melting	  temperature(Seko et	  al.,	  PRB	  2014)• Apply	  Bayesian	  optimization	  (BO)	  to	  discover	  the	  one	  with	  highest	  melting	  temperature	  from	  226	  materials	  • Initially,	  5%	  of	  materials	  are	  chosen	  randomly	  and	  their	  melting	  temperatures	  are	  observed• After	  that,	  next	  point	  to	  observe	  is	  determined	  by	  BODescriptors
DFT	  Calculated	  Features

Elemental	  Features

Cohesive	  Energy
Bulk	  modulus
VolumeNearest-­‐neighbor	  pair	  distanceComposition
Atomic	  number
Atomic	  mass	  Number	  of	  valence	  electrons
Group
PeriodVan	  del	  Waals	  radius
Covalent	  radiusElectronegativity
First-­‐ionization	  energy

Prediction	  Accuracy	  Open	  circle:	  Training	  examples
Closed	  circle:	  Test	  examples

Melting  Temperature

3500

3000

2500

2000

1500

1000

500

randomkriging
050

100150Materials  Examined

200250Number	  of	  measurements	  required	  to	  find	  the	  solid	  of	  highest	  melting	  temperature

Designed
16.1

Random133.4•AlBr3	  -­‐ As4S4	  -­‐ GeSe -­‐ Se	  -­‐ BaSe -­‐ SnO2	  -­‐ Sb2S3	  -­‐ Sb2Te3	  -­‐ Pb -­‐ SnF2	  -­‐ GeBr2	  -­‐ SnSe2	  -­‐ BaO -­‐ BaS -­‐ SrSe -­‐ SiC -­‐ BeO -­‐ [AlN]	  -­‐ Be3N2	  -­‐ Al2O3	  -­‐ Si3N4	  -­‐ Al4C3	  -­‐ MgO -­‐ CaO-­‐ CaC2	  -­‐ LiH -­‐ Cs	  -­‐ Be	  -­‐ BaH2	  -­‐ Bi2O4	  -­‐ K	  -­‐ BeF2	  -­‐ Tl -­‐ RbN3	  -­‐ LiF -­‐ PbTe -­‐ CsI -­‐ Li	  -­‐ P2O5	  -­‐ Tl2O3	  -­‐ BaF2	  -­‐ Bi	  -­‐ Ba -­‐ CaS -­‐ SrO -­‐ CaSi -­‐ PbO -­‐ CaF2	  -­‐ Rb -­‐ MgH2	  -­‐ Si	  -­‐ BaSi2	  -­‐ IBr -­‐Bi2O3	  -­‐ SrS -­‐ NaF -­‐ Ga2O3	  -­‐ Al	  -­‐ TlI -­‐ CsO2	  -­‐ KCl -­‐ In	  -­‐ I2	  -­‐ BiF3	  -­‐ SrF2	  -­‐ LiCl -­‐ InN -­‐ CsBr-­‐ ICl -­‐ SrH2	  -­‐ Pb3O4	  -­‐ Na	  -­‐ Na2O2	  -­‐ In2O3	  -­‐ RbI -­‐ S	  -­‐ PbF2	  -­‐ Bi2Te3	  -­‐ Sn -­‐ CaH2	  -­‐ KF	  -­‐InSb -­‐ Ca	  -­‐ BiI3	  -­‐ CsCl -­‐ K2O2	  -­‐ MgF2	  -­‐ Ge -­‐ PbS -­‐ SrSi2	  -­‐ TeO2	  -­‐ TlSe -­‐ Sr -­‐ BaI2	  -­‐ AlP -­‐Li2O	  -­‐ RbO2	  -­‐ CsF -­‐ P4S3	  -­‐ BiF5	  -­‐ Mg	  -­‐ GeO2	  -­‐ NaCl -­‐ CaSi2	  -­‐ BaCl2	  -­‐ Te	  -­‐ PbSe -­‐ TeF4	  -­‐PbI2	  -­‐ TlF -­‐ KI	  -­‐ P	  -­‐ MgS -­‐ SnTe -­‐ NaO2	  -­‐ GaAs -­‐ RbCl -­‐ Tl2O	  -­‐ SiS2	  -­‐ KO2	  -­‐ InAs -­‐ BaBr2	  -­‐ P2S3	  -­‐ Sb -­‐ KBr -­‐ TeI4	  -­‐ Li3N	  -­‐ TeO3	  -­‐ RbBr -­‐ SiI4	  -­‐ LiBr -­‐ GaSb -­‐ TlCl -­‐ SeO3	  -­‐ GaP -­‐RbF -­‐ SnI4	  -­‐ Cs2O	  -­‐ As2O3	  -­‐ SrCl2	  -­‐ Mg2Si	  -­‐ TlBr -­‐ AlAs -­‐ LiI -­‐ P4S7	  -­‐ Bi2S3	  -­‐ Mg2Sn	  -­‐CaCl2	  -­‐ AlI3	  -­‐ As2O5	  -­‐ SnSe -­‐ Ca3N2	  -­‐ Li2S	  -­‐ NaBr -­‐ InI3	  -­‐ BeCl2	  -­‐ Sb2O3	  -­‐ NaI -­‐Mg2Ge	  -­‐ InI -­‐ BiBr3	  -­‐ GeS -­‐ BeI2	  -­‐ SeBr4	  -­‐ Tl2S	  -­‐ InP -­‐ GaTe -­‐ P2S5	  -­‐ SbF3	  -­‐ K2S	  -­‐ BiCl3	  -­‐ SrBr2	  -­‐ InF3	  -­‐ GeTe -­‐ SbI3	  -­‐ AlSb -­‐ In2Te3	  -­‐ GeF2	  -­‐ Mg3Sb2	  -­‐ SrI2	  -­‐ PbCl2	  -­‐ GaS -­‐ PI3	  -­‐ Na2S	  -­‐ SnS -­‐ Al2S3	  -­‐ GaI3	  -­‐ Rb2S	  -­‐ GaSe -­‐ MgCl2	  -­‐ TeCl4	  -­‐ Rb2Se	  -­‐ PbBr2	  -­‐ GeI4	  -­‐K2Se	  -­‐ CaI2	  -­‐ BeBr2	  -­‐ P2I4	  -­‐ Sb2Se3	  -­‐ CaBr2	  -­‐ As2Te3	  -­‐ In2Se3	  -­‐ AlCl3	  -­‐ InS -­‐ GeBr4	  -­‐As2S3	  -­‐ Ga2Se3	  -­‐ SnBr4	  -­‐ InCl -­‐ As2Se3	  -­‐ AsBr3	  -­‐ AsI3	  -­‐ GaBr3	  -­‐ Al2Te3	  -­‐ In2S3	  -­‐SbBr3	  -­‐ MgI2	  -­‐ InBr3	  -­‐ GeS2	  -­‐ MgBr2	  -­‐ Ga2S3	  -­‐ GaCl3	  -­‐ SbCl3	  -­‐ SnBr2	  -­‐ GaCl2	  -­‐ SnCl2	  -­‐

Grain  boundary  structure  determination  1.5dy

1.4

1.3dz

1.2

1.1dx

1.0

8.0

3.0
6.0

2.0
4.0

1.0

2.0
0.0

0.0

Choose	  optimal	  translation	  parameters	  (dx,	  dy,	  dz)	  to	  minimize	  the	  grain	  boundary	  energy	  32Acceleration	  of	  Discovery
Cu	  [001]	  (210)	  Σ5	  grain	  boundary(a)(b)
Conventional method

1.5

GB Energy /J/㎡

Kriging

1.0

Exhaustive	  calculations	  Bayesian	  optimization
0GB energy=0.96J/m2

Number	  of	  energy	  calculations	  ＝16,983

4000
8000
12000216000
GBenergy=0.96J/m
Number of calculations

Number	  of	  energy	  calculations＝69S.	  Kiyohara et	  al.,	  Jpn.	  J.	  Appl.	  Phys.,	  2016.

33

Design nanostructures for phonon transport
via material informatics
Interface	  structure	  design	  has	  wide	  application	  in	  thermal	  devices.	  
High  ConductanceInterface  materials

Low  Conductance

Thermoelectricq various	  parameters	  q parameters	  effect	  coupledq transport	  vs	  local	  atomic	  configurationsq interference/resonance	  effects	  Thermal  barrier  coating
Ø low  developing  efficiencyØ high  experimental  costØ long  calculation  time

Department	  of	  Mechanical	  Engineering, Thermal	  Energy	  Engineering	  Lab34

Alloy	  Structure	  Optimization
Question: How to organize 16 alloy atoms (Si: 8, Ge: 8) to obtain the largest andsmallest interfacial thermal conductance?

311 151 5 9 134 8 12 16
2 6 10 14yz Lead
Descriptors: C168 = 12,870
Case 1 2 3 4
11 1 1 121 1 1 131 1 1 1… … … … …

7Si/Ge alloy region
5111…

6111…

7111…

8100…

90
10…

Lead

10 11 12 13 14 15 160 0 0 0 0 0 0
0 0 0 0 0 0 0
1 0 0 0 0 0 0… … … … … … …

Calculator: Atomistic Green’s Function (AGF): Phonon transmission
Evaluator: Interfacial Thermal Conductance (ITC)
Optimization method: Bayesian Optimization
Department	  of	  Mechanical	  Engineering, Thermal	  Energy	  Engineering	  Lab35

Alloy	  Structure	  Optimization
ITC

Si-Si

Si-GeMax
MinOptimal	  structures	  were	  obtained	  by	  calculating	  only	  3.4%	  of	  all	  candidates.
Department	  of	  Mechanical	  Engineering, Thermal	  Energy	  Engineering	  Lab36

Superlattices	  Structure	  OptimizationTopic: Arrange 10-layer superlattices structure (5 layers Si + 5 layers of Ge) between
Si and Si to obtain minimal thermal conductance (1 layer thickness = 5.43 A)

Si/Ge superlattice region

Lead
Descriptors:

C105 = 252
341
11
1
1
1…
…

Case
12
1
1
12
1
1
3
1
1…
…
…
Best Structure: (1101010001)

5100…

6010…

7001…

8000…

Department	  of	  Mechanical	  Engineering, Thermal	  Energy	  Engineering	  LabLead
9000…

10000…

37RNA	  Inverse	  Folding• Design	  RNA	  whose	  structure	  matches	  target• 4n candidates:	  Too	  many	  for	  Bayesian	  Opt

Target Structure

AAAAGUAAACAAUAUUAUUGUCAUGAAUUCCUUUUUUAUUGGGAUAAUACUUUAMonte	  Carlo	  Tree	  SearchMonte	  Carlo	  Tree	  Search• Candidates	  at	  leafs	  of	  search	  tree
• Reward	  at	  leafs:	  Similarity	  to	  target	  struc• Score	  at	  intermediate	  node	  by	  Playout– Random	  traverses	  to	  leafs– UCB	  score:	  Average	  reward	  +	  Penalty

Comparison	  with	  antaRNA

Conclusion• Artificial	  intelligence	  techniques	  combined	  with	  first	  principles	  calculation	  have	  enormous	  power	  Experimental	  Design

Artificial	  Intelligence

Simulation(DFT	  etc)
Features

Experiments