Kazuto Akagi AIMR, Tohoku University/NIMS

Activity Summaryof Topological Analysis Group

MI2I 最終報告会 19-20 February 2020 @一橋講堂

MaterialsresearchbyInformationIntegration”Initiative

赤木 和人（GL、東北大学） 平岡 裕章（SGL、京都大学） 小串 典子（NIMS／京都大学）

トポロジカルデータ解析の 理論・計算手法開発・応用展開

小原 真司（SGL、NIMS） 小野寺 陽平（京都大学） 田原 周太（琉球大学） 増野 敦信（弘前大学）

実験と計算機シミュレーションによる非晶質材料の作成・解析・モデリング

→　非晶質の物性を理解するための本質的な記述の発見 →　材料データベースの基盤デザイン →　材料特性の支配要因の抽出 →　HomCloud の開発、応用

トポロジカル解析グループ

小嗣 真人（東京理科大学）

トポロジカル機械学習手法の磁性材料課題への展開

HomCloud 大林・平岡

定量的で検索性が良い構造記述子を生成して 「中身が見える」逆問題アプローチを行う

vector data

! !

? ?

複雑な構造データ

組成

プロセス条件

環境の履歴

材料特性１

材料特性２

材料特性３新しい構造記述子

目指しているもの

input outputgeometric object PH�

metric info. of -dim holes�

input: hemoglobin output: persistence diagram (PD)

0 5 10 15 200

5

10

15

20

_ (birth)

_ (d

eath

)

� = 1

Yasuaki Hiraoka

connectivity, ring, cavity, ...

Persistent Homology — Mathematical tool treating “shape” of discrete data

an example for ℓ=1 (ring)b1 = 1.39 Å

(b2,d2)

(b1,d1)

Persistence diagram = Fingerprint of the "shape" in discrete data summarized as a 2-D histogram

・Born at r=b, dead at r=d ・Each (b,d) represents each "Hole" ・Robust "Hole" : apart from the diagonal line ・Noisy "Hole" : near by the diagonal line

d1 = 1.51 Åb2 = 1.52 Å d2 = 2.02 Å

Voronoi devision

Persistent Homology — Mathematical tool treating “shape” of discrete data

# of

pap

ers

0

20

40

60

80

100

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

1022123121 0materials science →

Publication on "Persistent Homology" (Web of Science)

秩序に気づく

Nakamura, H. et al. Nanotechnology 26 (2015)

−10−5

05

1015

−5

0

5

10−15

−10

−5

0

5

10

crystalliquid

05

1015

2025

05

1015

20250

5

10

15

20

25

30

glass

05

1015

2025

05

1015

20250

5

10

15

20

25

30

Application to SiO2

Detection of "hidden" order

Spatial ordering analysis of specific atomic groups (a kind of coarse graining)

Free volume analysis combined with positron annihilation measurement

Detection of hidden order in “amorphous” structure

Forward and Inverse Analysis based on Persistent Homology

Input Data Descriptor

・Good affinity with machine-learning

・Database of complex systems

system 1

system 2

system N

(properly translated vector data)

Atomic Configuration

Image Data

Persistence Diagram

• Extraction of hidden order

• Finding correlation with various properties • Elucidation of key structures in original data

違いを調べる、分類する

- target: metallic glass (Pd80Si20) - identify structural changes induced from cooling rates - apply PDs to MDs for describing structures - combine ML and inverse analysis for explicitly identify those changes

PD of PCA1 (Si, dim=1)PD of PCA1 (Pd, dim=2)

Pd, dim=2

PCA1

PCA

2

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Metallic Glass: cooling rate effect on glass structures （平岡、大林、平田）

Metallic Glass: cooling rate effect on glass structures

PD of PCA1 (Si, dim=1)PD of PCA1 (Pd, dim=2)

Pd, dim=2

PCA1

PCA

2

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1011K/sec<latexit sha1_base64="gmE3sXcl2cWHc3xLBPi0yYztD84=">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</latexit><latexit sha1_base64="gmE3sXcl2cWHc3xLBPi0yYztD84=">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</latexit><latexit sha1_base64="gmE3sXcl2cWHc3xLBPi0yYztD84=">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</latexit><latexit sha1_base64="gmE3sXcl2cWHc3xLBPi0yYztD84=">AAACdnichVHLSsNAFD2N7/qquhFcWCxVV/VGBB8rwY3gplqrgo+SxKkG8yJJixr6A/6AC0FQkCp+hht/wEU/QVwqiODC2zQgKuodZubMmXvunJlRHUP3fKJaTGpqbmlta++Id3Z19/Qm+vrXPLvkaiKv2YbtbqiKJwzdEnlf9w2x4bhCMVVDrKsHC/X99bJwPd22Vv0jR2ybyp6lF3VN8ZkqJPpl2glkuRJsuWZyacITWqWQSFGGwkj+BHIEUogiayeq2MIubGgowYSABZ+xAQUet03IIDjMbSNgzmWkh/sCFcRZW+IswRkKswc87vFqM2ItXtdreqFa41MM7i4rk0jTA93QM93TLT3S+6+1grBG3csRz2pDK5xC78lg7vVflcmzj/1P1Z+efRQxE3rV2bsTMvVbaA19+fj0OTe3kg5G6ZKe2P8F1eiOb2CVX7SrZbFyhjh/gPz9uX+C/GRmNiMvT6Xmp6KfaMcQRjDOzz2NeSwiizwfe4hzVHEde5OGpbQ01kiVYpFmAF9Cog/jIpBC</latexit>

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Inverse of PCA explicit identifies geometry affected by cooling rates!

（平岡、大林、平田）

δx δyδz

x

yz

Mg

O

Model: MgO (310) Σ5 Grain boundary

*丸のサイズ: 出現頻度

*色: 多面体のエネルギー

粒界のコストを各(bk,dk)を与える最小サイクル Zkのエネルギー（Coulomb＆van der Waals）で評価

最安定構造の候補（上位1%）例）(δx, δy, δz) = (0.0, 2.1, 1.7)

• 上δx δy

δz(2) (1) (3,4)

-0.4

0

0.4

0.8

1.2

1.6

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Ener

gy

Rank

4

5

6

-0.4

0

0.4

0.8

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Ener

gy

Rank

4

5

6

2) van der Waals

1) Coulomb

（小串）

粒界構造を系統的に生成

Evaluation of Interface Structure

変化を捉える

0 ps 20 ps 50 ps

1

2

3

4

0.5 1.0 1.5 2.0 2.5 [Å]

0 ps20 ps50 ps

r/2 decimation = 0 %

0 ps - 20 ps 20 ps - 50 ps

triangle in6-membered ring

interlayerorder

decimation = 50 %

Amorphous carbon at high-temperature MD

6-memberedring

5-memberedring

trianglein 6-membered ring

interlayerorder

7-memberedring

10 20 30 40 50Time [ps]

10 20 30 40 50Time [ps]

6-membered ring

5-membered ring

7-membered ring

3-membered ring4-membered ring

8-membered ring

Interlayer order can also be quantified based on PD.

Quantification of Structural Motifs

conventional ring analysis# of generators in PD

0-18 ps

19-24 ps

25-32 ps33-40 ps

40-100 psPC2 vector

PC1 vector

6員環の増減

7員環の増減

Detecting transformation of ring structures

PCA of PD1

実材料の解析

ガラスの構造の本質を探る

SiO4 tetrahedron

SiO6 octahedron

Novel Structure in Oxide Glass

Transition from tetrahedral SiO4 to octahedral SiO6 (PD2)

（小原、小野寺、増野、田原）

Yellow：Si Red：Bridging O (BO) Blue：Non-bridging O (NBO) Cyan：R＝Na, K

KO5(2NBO+3BO)

KO6(2NBO+4BO)

NaO4(2NBO+2BO)

NaO5(2NBO+3BO)

KO6(2NBO+4BO)

Four-membered ringswith R2NBO2 are detected by TDA→ Getting aware of hidden correlation between Na and K

δ-R+

δ-R+

R2Oremove one BO put two NBO

Two alkali ions are trapped around these two NBO to compensate negative charge.

Information beyond “pair-correlation” plays an important role!

Structural origin of mixed alkali effectin alkali silicate glass

（小原、小野寺、増野、田原）

磁区構造から情報を取り出す

保磁力

欠陥によるピンどめ

磁気ヒステリシス(巨視的解析)磁区構造

（微視的解析）

保磁力：発電効率に直結する磁気機能

モーター

(BH)max=Br×Hc

保磁力最大ｴﾈﾙｷﾞｰ積

高性能磁石（硬磁性材料）　高い保磁力が必要

鉄芯（軟磁性材料）低い保磁力が必要

保磁力マクロな物理量

磁区構造ミクロな磁気結合

対応関係は未だ完全に解明されていない。

結晶粒磁区構造粒界厚さ磁気異方性磁化

磁化反転に必要な外部磁場

電気自動車

モーターの構造（例）

保磁力の支配要因の可視化 （小嗣）

birth

deat

h

Magnetic Field (Oe)

Mag

netiz

atio

n (n

orm

aliz

ed)

-200 -100 0 100 200

-1

0

1 非平衡相

平衡相

磁気ヒステリシスループ PCA loadingから作成したPD

PDにおいて保磁力に寄与する非平衡相に相当する部分を同定

保磁力

保磁力近傍→ 磁化率が最も高い

→ 外部磁場変化に最も鋭敏

PDから元の磁区構造に逆解析

逆解析により迷路状磁区構造のトポロジカル欠陥を可視化

Generatorを逆解析

磁場変化に鋭敏なPDを生成 保磁力近傍の

PDを包含

非平衡成分のマッピング （小嗣）

パーシステンス図と主成分分析を用いたピニングサイトの可視化

磁区構造のパターン自体は毎回異なるが、「トポロジカル欠陥」の場所を積算してみると

格子欠陥の近傍がピンニングサイトになっている様子がわかった

（小嗣）

構造を「測る」 Ⅰ

dark part : α-phase (hcp structure) bright part : β-phase (bcc structure)

(provided by KOBELCO）SEM image of forged Ti alloy

Quantitative characterization by inverse analysis of persistence diagram

・複雑な画像をコンパクトに記述・特徴ごとに定量化・不均一性の抽出

Machine Learning

Primitive Descriptor

(100-dimension vector)

⋮

area 1

area N⋮

Persistence Diagram (PD)

a set of PDs from massive small cells

scan

area 1

area N PC1 PC2 PC3

Different characterization by different feature values

Quantitative characterization by PCA of local structures via persistence diagram

画像内の局所構造の分布を自動抽出＆可視化

構造を「測る」 Ⅱ

Can we distinguish TEM images of amorphous Ge?

Sample1

Sample2

（Xu）

Appropriate pre-conditioning Si substrate

Sample1

without pre-conditioning

Binarized PD0 PC1

Averaged Brightness

Binarized PD1 PC1

Sample1

Sample2

Sample3

with pre-conditioning

Sample1

Sample1

Binarized PD0 PC1

Binarized PD0 PC1

Binarized PD0 PC1

輝度情報が前面に出る（欲しい情報ではない） 「形」の情報に基づく分類

HomCloud

Search now “HomCloud AIMR” !

HomCloud パッケージの開発 （大林、平岡）

・原子配置や画像データ（2D,3D）を入力・パーシステント図の計算（順解析）・(b,d)点に対応する構造を入力データにマップ （逆解析）・Python による実装・GPL v3 の下での公開

HomCloud コミュニティーの立ち上げへの要望

•普及と啓蒙（理解の向上、誤解の解消）

•適用事例の集積と共有

•「足りないもの」を見つける（学術側・産業側の両面で）

• HomCloudの継続的な開発を支援

•窓口を明確化

開発中心のフェーズから応用展開のフェーズへ 　→ 共同研究の内容の深化 　→ プロジェクトを通した「社会実装」

一方、「使ってみたけれど...」の声も多数

参加に関心のある方（企業、研究者個人）は赤木までご連絡ください 　→ akagi@wpi-aimr.tohoku.ac.jp

ひとまず、皆様のご支援に感謝！