Machine Learning for Molecules

Machine Learning for Molecules
Ichigaku Takigawa
takigawa@icredd.hokudai.ac.jp
15 October 2021 @ Hokkaido University
Hokkaido Univ ICReDD-Faculty of Medicine Joint Symposium

/ 23
2
RIKEN Center for AI Project @ Kyoto
Medical-risk Avoidance based on iPS Cells Team
(A joint lab with Kyoto Univ CiRA)
Inst. Chemical Reaction Design & Discovery
Hokkaido Univ
A machine learning (ML) researcher working for
ML for Stem Cell Biology ML for Chemistry

/ 23
2
Hokkaido Univ
Interests: Machine Learning and Machine Discovery
An intersection of ML with combinatorial structures + ML for natural sciences

/ 23
2
Hokkaido Univ
Interests: Machine Learning and Machine Discovery
An intersection of ML with combinatorial structures + ML for natural sciences
Joint project with HU Med Dept:
• Prof. Shinya Tanaka: Cancer diagnosis with ﬂuorescent markers, Enzyme-catalyzed reaction design
• Prof. Shigetsugu Hatakeyama: Mediator complex of transcription regulations (Nat Commun 2020, 2015)
• Prof. Ichiro Yabe: Video-based predictions of motor symptom severity
• Prof. Yasuyuki Fujita: Cell competition (Cell Reports 2018; Sci Rep 2015)
• Prof. Hidenao Sasaki: Copy number variations for neurodegenerative diseases (Mol Brain 2017)

/ 23
3
X-informatics: Bio- and Chemo-informatics
• Biochemical reaction networks (Metabolic pathways)
Bioinformatics 2007, 2008a, 2008b, 2009, 2010
Nucleic Acids Res 2011, PLoS One 2012, 2013, KDD’07
• Drug-target interactions (Polypharmacology)
PLoS One 2011, Drug Discov Today 2013, Brief Bioinform 2014
• Modulatory proteolysis
Mol Cell Proteom 2016, Genome Informatics 2009
(We also developed a database http://calpain.org)
• Genomic repeats
Discrete Appl Math 2013, 2016, AAAI 2020
• Genetic variations in cancer cells
Brief Bioinform 2014
• Mediator complex and transcription regulation
Nat Commun 2015, 2020 (w/ Prof. Hatakeyama)
• Genomic copy number variations for neurodegenerative diseases
Mol Brain 2017 (w/ Prof. Sasaki)
• Cell competitions and cancer cells
Cell Reports 2018, Sci Rep 2015 (w/ Prof. Fujita)
In addition to pure ML research, I’ve worked for bio/chemo-informatics

/ 23
4
Molecules have a combinatorial aspect
https://cen.acs.org/physical-chemistry/computational-chemistry/Exploring-chemical-space-AI-take/98/i13

/ 23
5
simulation
ML: A new way for (lazy) programming
computer program
input output
full speciﬁcation in
every detail required
deductive (rationalism)

/ 23
5
simulation
computer program
input output
input output
computer program
ML
give up explicit model
instead, grab a tunable
model, and show it many
input-output instances
inductive (empiricism)
airhead with a god-like
learning capability
Random Forest Neural Networks SVR Kernel Ridge
All about fitting a very-flexible function to finite points in high-dimensional space.

/ 23
6
x1
x2
y
p1 p2 p3 p5
p4
All about statistical and algorithmic techniques for
surface-model ﬁtting to data points by adjusting model parameters.
Variable 1
Variable 2
<latexit sha1_base64="Ill3Als4zZd947f5Xm9sW99d0QA=">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</latexit>
x1
<latexit sha1_base64="QFtMwnKe2I12XGZu0bNJbdnDaaE=">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</latexit>
x2
x1
x2
x1
x2
y
ML
ML = Tweak these parameter values to
best ﬁt a surface model to the given points.
5 params

/ 23
7
A modern aspect of ML
ResNet50: 26 million params
ResNet101: 45 million params
EfficientNet-B7: 66 million params
VGG19: 144 million params
12-layer, 12-heads BERT: 110 million params
24-layer, 16-heads BERT: 336 million params
GPT-2 XL: 1558 million params
GPT-3: 175 billion params
Modern ML: Can we imagine what would happen if we try to fit a function having 175
billion parameters to 100 million data points in 10 thousand dimension??
simulation
input output
computer program
input output
computer program
ML
give up explicit model
instead, grab a tunable
model, and show it many
input-output instances
inductive (empiricism)
airhead with a god-like
learning capability
All about fitting a very-flexible function to finite points in high-dimensional space.

/ 23
8
This Talk: ML for Molecular Graphs
Latent
variables
Representation
learning
Reactions
Materials
Molecules
Graphs (of different size)
Node
features
Edge
features
CC1CCNO1
Graph Neural
Networks (GNNs)
NCc1ccoc1.S=(Cl)Cl>>[RX_5]S=C=NCc1ccoc1
…
Classiﬁer or
Regressor
Diverse
Downstream
Tasks
Modular Hierarchy
Amide
Proline
Oxazoline
Compositionality
Phenyl
Carboxyl Methyl Ethyl Tert-butyl
Isoprophyl
Trifluoromethyl
Benzyl
Substituents
Graph 
Coarsening
Combinatorial aspects

/ 23
9
Representation Learning
Use some inductive biases to constrain/regularize the model space.
Prediction
Input
variables
Classiﬁer or
Regressor
x1
x2
<latexit sha1_base64="lFhRrRrVTrFR31ebbMgRp5myJpc=">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</latexit>
x3
<latexit sha1_base64="0IPXcU0UIDvzZlYURjV2A/THv9U=">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</latexit>
.
.
.
Function
model

/ 23
10
Prediction
Input
variables
Function
model
x2
x3
.
.
.
Latent
variables
Learnable variable
transformation
Representation learning
Classiﬁer or
Regressor
x1

/ 23
10
Prediction
Input
variables
Function
model
x2
x3
.
.
.
Latent
variables
Learnable variable
transformation
Representation learning
Classiﬁer or
Regressor
Linear
x1
Simple model is enough
when we have good features.

/ 23
11
Use Case 1: Virtual Screening (QSAR/QSPR)
• Mutagenic potency
• Carcinogenic potency
• Endocrine disruption
• Growth inhibition
• Aqueous solubility
N
NH
O
O
H
H
H
H H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
O
O
O
O
O
O
Cl
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
Br
Br O P
O
O Br
Br
O
Br
Br
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
N
S
N
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
O
N
O
O
H
H
H
O
O
H
H
N
O
O
Cl
Cl
Cl
H
H
H
H
H
H H
N
O
O
H
H
H
H
H
H
H H
H
N
O
O
H
H
H
H
H
H
H
N
H
N
O
O
N
O
O
H
H
H
H
H
H
H
H
N
CH3
O
O
H
N Cl
Cl
Cl
Cl
Cl
H3C
O O
O
O
O
O
H3C
CH3
CH2
O
HN
O
O
NH
CH3
HO
OH
CH3
N
O
O
CH3
N
N
H
N
H
H3C
N
H3C
H3C
NH
O
N
O
N
O
CH3
O N
NH2
O
CH3
Br
CH3
N
H3C
H
N
S
N
O
CH3
N
OH
CH3
CH3
N
N
N
CH3
H3C
H2N NH2
H
OH
O
HO
CH3
H
H
O
CH3
H
O
O
H3C H
H
H
O
H3C
S
CH3
O
H
H
O
CH3
CH3
O
O
HO
H3C
H
HO
F
H
O
H3C
NH2
O
N
HO
H
O
O
H
H
O
O
O
H3C
O
O
O
CH3
O
CH3
H
O
CH3
H
O
O
CH3
H
H
N
H
N O
H3C
O
O
O

/ 23
12
https://pubchem.ncbi.nlm.nih.gov/bioassay/1

/ 23
13
input output
ML
activity: “Active”
LogGI50: -7.8811
CID 11978790
GI50: concentration required
for 50% inhibition of growth

/ 23
14
Input representation (molecular graph)
1
2
1
3
explicit Hs
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Any permutation of
this numbering should
not change the results.
❗
CID 204
atoms → nodes
bonds → edges
1. permutation
equivariance
2. permutation
invariance

/ 23
14
1
2
1
3
explicit Hs
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Any permutation of
❗
CID 204
• atomic_num (one-hot, 101)
• total_degree (one-hot, 7)
• formal_charge (one-hot, 6)
• chiral_tag (one-hot, 5)
• num_Hs (one-hot, 6)
• hybridization (one-hot, 6)
• is_aromatic (binary, 1)
• atomic_mass (real, 1)
17
edge(bond) features
• no_bond (binary, 1)
• is_single (binary, 1)
• is_double (binary, 1)
• is_triple (binary, 1)
• is_connjugated (binary, 1)
• is_in_ring (binary, 1)
• stereo (one-hot, 7)
17
14
133
node(atom) features
133 features 14 features
e.g. Features for ChemProp (Yang et al, 2019)
atoms → nodes
bonds → edges
1. permutation
equivariance
2. permutation
invariance

/ 23
14
1
2
1
3
explicit Hs
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Any permutation of
❗
atom features bond features
topology
Molecular Graph
read out
graph-level
output
• sum, mean or max
• attentive pooling
CID 204
• atomic_num (one-hot, 101)
• total_degree (one-hot, 7)
• formal_charge (one-hot, 6)
• chiral_tag (one-hot, 5)
• num_Hs (one-hot, 6)
• hybridization (one-hot, 6)
• atomic_mass (real, 1)
17
edge(bond) features
• no_bond (binary, 1)
• is_single (binary, 1)
• is_double (binary, 1)
• is_triple (binary, 1)
• is_connjugated (binary, 1)
• is_in_ring (binary, 1)
• stereo (one-hot, 7)
17
14
133
node(atom) features
133 features 14 features
e.g. Features for ChemProp (Yang et al, 2019)
atoms → nodes
bonds → edges
1. permutation
equivariance
2. permutation
invariance

/ 23
15
Graph Neural Networks (GNNs)
N O
C
C
C
C
H
H
H
H
H
N O
C
C
C
C
H
H
H
H
H
GNN Layer
GNN updates
features

/ 23
15
N O
C
C
C
C
H
H
H
H
H
N O
C
C
C
C
H
H
H
H
H
GNN Layer
GNN updates
features
<latexit sha1_base64="+I1ZH8a510AHL/VRK05INyOdDHc=">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</latexit>
hi
<latexit sha1_base64="iVE2zwSrY7uMFp5lULN8y4s7ZXg=">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</latexit>
eij
atom features
bond features

/ 23
15
N O
C
C
C
C
H
H
H
H
H
N O
C
C
C
C
H
H
H
H
H
GNN Layer
GNN updates
features
<latexit sha1_base64="rQGx6XMOvsCjXRp7b9gbmKjgm1M=">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</latexit>
hi
0
@hi,
M
j2Ni
(hi, hj, eij)
1
A
Update by “Message Passing”
hi
eij
atom features
bond features

/ 23
15
N O
C
C
C
C
H
H
H
H
H
N O
C
C
C
C
H
H
H
H
H
GNN Layer
GNN updates
features
Message
Permutation
equivariant
operations
• nn.Linear
Bond features can be
used (typically in )
hi
0
@hi,
M
j2Ni
(hi, hj, eij)
1
A
hi
eij
atom features
bond features

/ 23
15
N O
C
C
C
C
H
H
H
H
H
N O
C
C
C
C
H
H
H
H
H
GNN Layer
GNN updates
features
Aggregate
Permutation
invariant
operations
Message
Permutation
equivariant
operations
• nn.Linear
hi
0
@hi,
M
j2Ni
(hi, hj, eij)
1
A
hi
eij
atom features
bond features

/ 23
15
N O
C
C
C
C
H
H
H
H
H
N O
C
C
C
C
H
H
H
H
H
GNN Layer
GNN updates
features
Aggregate
Permutation
invariant
operations
Update
Any
• nn.Linear
Message
Permutation
equivariant
operations
• nn.Linear
hi
0
@hi,
M
j2Ni
(hi, hj, eij)
1
A
hi
eij
atom features
bond features

/ 23
16
ChemProp
(Directed MPNN)
ExtraTrees
w/ ECFP6(1024)
Performance for unseen (test) data:
Standard ML GNN
Stokes et al, Cell (2020) https://doi.org/10.1016/j.cell.2020.01.021
Marchant, Nature (2020) https://doi.org/10.1038/d41586-020-00018-3
ChemProp (Yang et al, 2019)
from MIT MLPDS (Machine Learning
for Pharmaceutical Discovery
and Synthesis) Consortium
Disclaimer: This is just for a toy demo. This should be taken
as classification for ACTIVITY_OUTCOME (Active or Inactive)
95.079% (Active/Inactive) 95.604% (Active/Inactive)
• Regression for LogGI50 • Regression for LogGI50
• Classification accuracy • Classification accuracy
RMSE 0.6076
RMSE 0.7970
Activie/Inactive (Classification), LogGI50 (Regression)

/ 23
17
https://qcarchive.molssi.org/apps/ml_datasets/
Use Case 2: Quantum chemistry

/ 23
18
input output
gdb_21014
1000 sec
Density Functional Theory (DFT)
B3LYP/6-31G(2df, p)
<latexit sha1_base64="JI//afsBt1AdIhSgVUbVSGVXtww=">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</latexit>
Ĥ = E
by solving a one-electron Schrödinger
equation (Kohn–Sham equation)
Quantum chemical
calculations

/ 23
18
input output
gdb_21014
1000 sec
Density Functional Theory (DFT)
B3LYP/6-31G(2df, p)
<latexit sha1_base64="JI//afsBt1AdIhSgVUbVSGVXtww=">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</latexit>
Ĥ = E
by solving a one-electron Schrödinger
equation (Kohn–Sham equation)
ML
0.01 sec
≈
100,000 times faster!
Quantum chemical
calculations

/ 23
19
input molecule H2O
gdb_3
0
1 2
graph (SchNet)
0 1
atom features

0 1 2
2
edges w/ cutoff (10Å)
0
bond features
0 1
1
0 2
2
1 2
edge_index
0.9620 0.9622 1.5133
latexit sha1_base64=WhwbZjIo+PbaHz7kU/YZBO38PiQ=AAACp3ichVG7SgNBFD2u72eiNoLNYlC0MEwkqAhC0MbO+EgMGFl211En2Re7m4Cu6cUfsLBSsBDBVnsbf8DCTxBLBRsLbzYLoqLeZXbOnLnnzpm5mmMIz2fssUlqbmlta+/o7Oru6e2LxfsH8p5dcXWe023Ddgua6nFDWDznC9/gBcflqqkZfEMrL9b3N6rc9YRtrfv7Dt8y1V1L7Ahd9YlS4iOuEohSTZ6bl4uHRc0M3Joi5Ek5giVilXiCJVkY8k+QikACUWTt+A2K2IYNHRWY4LDgEzagwqNvEykwOMRtISDOJSTCfY4aukhboSxOGSqxZfrv0mozYi1a12t6oVqnUwwaLilljLIHdsle2D27Yk/s/ddaQVij7mWfZq2h5Y4SOx5ae/tXZdLsY+9T9adnHzuYDb0K8u6ETP0WekNfPTh5WZtbHQ3G2Dl7Jv9n7JHd0Q2s6qt+scJXT//wo5EXejFqUOp7O36C/FQyNZ1Mr6QTmYWoVR0YxgjGqR8zyGAJWeSo/hGucYNbaUJalvJSoZEqNUWaQXwJSf0AKaGdRg==/latexit
rij := kri rjk
latexit sha1_base64=kMmroSd0z/qeaFfqTkrtDbgltFg=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/latexit
Z0 = 8
latexit sha1_base64=QxdA1PVsyCLNE23CpTjm2APprYs=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/latexit
Z1 = 1
latexit sha1_base64=PJMbQqlxF/BaTgtbHwfwEQN8SrI=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/latexit
Z2 = 1
latexit sha1_base64=A/aHUcWCUQde6WVY9Df1h30Gjpk=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/latexit
r0 = [ 0.0344, 0.9775, 0.0076]
latexit sha1_base64=2hhG9gKLK2JIb9w0aH6ObiinRms=AAACpnichVHLSsNQED3GV3226kZwUy2KCykTqbUIgujGlfiqFWqpSbxqMC+StKDFteAPuHCl4ELErX6AG3/AhZ8gLhXcuHCSBkRFnZDMuefOmZx7R3UM3fOJHhukxqbmltZYW3tHZ1d3PNHTu+bZFVcTec02bHddVTxh6JbI+7pviHXHFYqpGqKg7s0F+4WqcD3dtlb9fUeUTGXH0rd1TfGZKicGN1Sz5h6W5eR0skhpymZyY5zGKRskkidK5UQqQEEkfwI5AilEsWgnbrGBLdjQUIEJAQs+YwMKPH6KkEFwmCuhxpzLSA/3BQ7RztoKVwmuUJjd4+8Or4oRa/E66OmFao3/YvDrsjKJYXqgS3qhe7qiJ3r/tVct7BF42ees1rXCKceP+1fe/lWZnH3sfqr+9OxjG7nQq87enZAJTqHV9dWDk5eVqeXh2gid0zP7P6NHuuMTWNVX7WJJLJ/+4UdlL3xjPCD5+zh+grXxtJxNZ5YyqZnZaFQxDGAIozyPScxgHovIc/8jXOMGt9KotCDlpUK9VGqINH34EtLmBwvLmR0=/latexit
r1 = [0.0648, 0.0206, 0.0015]
latexit sha1_base64=FqaYo7zlBtUvxlEmhgyAfxy/v8k=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/latexit
r2 = [0.8718, 1.3008, 0.0007]
SchNet (Schütt et al, 2017)
latexit sha1_base64=tzvRXqv2dAYIROlG6uwbJPf0mrw=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/latexit
xi xi +
0
@
X
j2Ni
(xj) !ij
1
A
Message Passing with
residual connections
latexit sha1_base64=4oqceeOsg0RegmHmCOLOjG0SaOU=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/latexit
x0
latexit sha1_base64=jqQfQ7TB6F1UPH31OFoS1eerzNw=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
x1
latexit sha1_base64=fLMd1ywDpT0cBkzaL9hTb77jq/8=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
x2
latexit sha1_base64=YVJW2X9s34FCmpunsQgR00z8vXY=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/latexit
w01
latexit sha1_base64=tYR7XnwyhyUSVK/6XFo1uz/tDtI=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/latexit
w02
latexit sha1_base64=Ak3wjfcp94hUo7DAHdEjDzlDdm0=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/latexit
w12

/ 23
19
input molecule H2O
gdb_3
0
1 2
graph (SchNet)
0 1
atom features

0 1 2
2
0
bond features
0 1
1
0 2
2
1 2
edge_index
0.9620 0.9622 1.5133
rij := kri rjk
Z0 = 8
Z1 = 1
Z2 = 1
r0 = [ 0.0344, 0.9775, 0.0076]
r1 = [0.0648, 0.0206, 0.0015]
r2 = [0.8718, 1.3008, 0.0007]
nn.Embedding
128
-1.249
1.6278
-0.1370
⋮
-0.9488
0.3105
-1.6185
0.1960
⋮
-0.5310
0.3105
-1.6185
0.1960
⋮
-0.5310
x0
x1
x2
xi xi +
0
@
X
j2Ni
(xj) !ij
1
A
w01
w02
w12

/ 23
19
input molecule H2O
gdb_3
0
1 2
graph (SchNet)
0 1
atom features

0 1 2
2
0
bond features
0 1
1
0 2
2
1 2
edge_index
0.9620 0.9622 1.5133
rij := kri rjk
50
MLP 50 →128
0.1803
0.0826
0.3349
⋮
-0.474
0.0403
-0.003
0.0802
⋮
-0.061
0.1803
0.0826
0.3349
⋮
-0.474
128
latexit sha1_base64=zybc8bdG60pci39izd8WqLQ5/Rk=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
exp( ↵(rij µ↵)2
)
Z0 = 8
Z1 = 1
Z2 = 1
r0 = [ 0.0344, 0.9775, 0.0076]
r1 = [0.0648, 0.0206, 0.0015]
r2 = [0.8718, 1.3008, 0.0007]
nn.Embedding
128
-1.249
1.6278
-0.1370
⋮
-0.9488
0.3105
-1.6185
0.1960
⋮
-0.5310
0.3105
-1.6185
0.1960
⋮
-0.5310
x0
x1
x2
Weighted ACSFs (ACSFs = atom-
centered symmetry functions)
for Behler-Parrinello potentials
latexit sha1_base64=bbWlQHipawsZwudry4/MYk1A7nU=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/latexit
1
2
✓
cos
✓
⇡rij
rc
◆
+ 1
◆
cutoff function
element-wise product
w01
w02
w12
xi xi +
0
@
X
j2Ni
(xj) !ij
1
A

/ 23
20
pred vs true for SchNet (Schütt et al, 2017)
pred vs true for DimeNet (Klicpera et al, 2020)
Dipole Moment Energy U
HOMO
LUMO
Heat Capacity
Enthalpy H
Dipole Moment Energy U
HOMO
LUMO
Heat Capacity
Enthalpy H

/ 23
21
DimeNet (Klicpera et al, 2020)
Free Energy Free Energy
y_true
y_true
y_pred y_pred
ExtraTrees w/ ECFP6 LightGBM w/ ECFP6 3-Layer MLP w/ ECFP6
(without 3D geometry) (without 3D geometry) (without 3D geometry)
Free Energy Free Energy Free Energy

/ 23
22
Chemical Reaction Design and Discovery
EQ1 EQ2
Chemical Reaction
How we can have this?

/ 23
22
EQ1 EQ2
Chemical Reaction

/ 23
22
EQ1 EQ2
Chemical Reaction
ML
Retrosynthesis
prediction
Forward Reaction
prediction

/ 23
Potential Energy Surface
latexit sha1_base64=Wyp4gB8RxRsto5OIPkBWRdHaY3U=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
E
latexit sha1_base64=VQOOvVSP0lW6m0gNVQ8zA5pNsEc=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/latexit
ri
latexit sha1_base64=kTQzD4iiA9afGMFuEz1PlDAJN4Y=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
rj
22
EQ1 EQ2
Chemical Reaction

/ 23
E
ri
rj
22
EQ1 EQ2
TS
Chemical Reaction

/ 23
E
ri
rj
22
EQ1 EQ2
TS
Chemical Reaction
Energy
E
ML
• Acceleration by ML potential?
• Artiﬁcial force learning?
ML
Forces
• Scope/network expansion?
ML
• Fill any gap between theory and
experiments (reality) by data?

/ 23
23
Machine Learning and Machine Discovery
• Machine Learning: many fascinating technical topics of my long-
standing interests on “ML with combinatorial structures” (such as GNNs)
• Machine Discovery: many long-standing important open problems
towards “AI for automating discovery”
Prior Info
Observational data
Reported facts
Textbook knowledge
Discovery
Representation
Model (Belief)
Intervention
Hypothesis
New Info
Prior Info
• Identify relevant variables
• Set design choices
• Set experiments
• Interpret results
Model (Belief)
Hypothesis
https://itakigawa.github.io/data/icred_med_202110.pdf
An exciting “real-world” test bench for ML researchers!
This Slide

Machine Learning for Molecules

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Ähnlich wie Machine Learning for Molecules

Ähnlich wie Machine Learning for Molecules (20)

Mehr von Ichigaku Takigawa

Mehr von Ichigaku Takigawa (20)

Kürzlich hochgeladen

Kürzlich hochgeladen (20)

Machine Learning for Molecules