Table 2 Number of multiple polycrystalline solutions of E11 with different number of real non-zero dimensions.

From: An AI-driven microstructure optimization framework for elastic properties of titanium beyond cubic crystal systems

No. of non-zero dimensions

≥2

≥3

Optimal target

Crystal System

ID

Threshold

Threshold

   

0.01%

0.1%

0.2%

0.5%

0.01%

0.1%

0.2%

0.5%

\({E}_{11}^{min}\)

Cubic

15716

10

112

227

559

0

0

0

5

Hexagonal

1028

253

2378

4858

14488

0

68

332

2292

1029

302

3013

6340

18668

1

83

401

2923

1030

315

3809

8119

24225

0

100

519

3865

14732

5937

59897

121391

319939

0

133

665

7284

14815

679

6152

12819

37890

1

181

833

6046

84837

813

6662

13567

39069

1

169

795

5587

84936

998

8762

18054

54057

1

285

1301

9448

\({E}_{11}^{max}\)

Cubic

15716

15785

26578

38765

58515

12

540

1511

8320

Hexagonal

1028

459

1773

3061

6530

5

51

131

571

1029

621

2372

4008

8223

1

52

170

761

1030

789

2898

4958

10390

1

69

209

955

14732

98

2115

4399

11568

0

24

135

819

14815

1455

5431

8999

18657

1

115

401

1797

84837

424

4216

7979

19230

0

67

308

1666

84936

2125

7162

11805

24658

7

176

581

2487