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Choice of priors

Choice of priors

Owned by Pavan Behara
Last updated: Feb 04, 2021
3 min read

ForceBalance reference paper: dx.doi.org/10.1021/ct300826t

Objective function (X2) to build the valence parameters using QM reference data with force balance is shown above (taken from the cited paper). Overfitting of parameters results in extreme values and Tikhonov regularization (or ridge regression) is applied in FB wherein a quadratic penalty is added to the obj. fn that restrains parameters to their initial values. Each parameter varies over a different length scale and hence each of them have different priors for regularization and dimension rescaling.

Simple Fit1

Starting from different values of priors, and with the same starting point for all, simple_fit1 converges to almost same values of parameters and the difference is negligible.

Simple Fit1

Prior = 0.2

Prior = 2

Prior = 5

Prior = 10





Obj. fn value Full

168.73

165.65

165.37

165.33





Un-penalised

168.28

165.36

165.32

165.31





Params trained













0

0.9642

0.9593

0.9590

0.9589

k1_bondorder1

[*:1]~[#6X3:2]~[#6X3:3]~[*:4]

1

5.0973

4.1120

4.0217

4.0071

k1_bondorder2

[*:1]~[#6X3:2]~[#6X3:3]~[*:4]

 

Fit 7

Starting from different values of priors, and with the same starting point for all, fit7 has significant diferences in parameters.

 

Fit 7

Prior = 0.2

Prior = 2

Prior = 5

Prior = 10









Obj. fn value (X2) Full

1557.11

1547.05

1541.46

1538.20









Un-penalised

1553.45

1544.52

1538.28

1536.80

Std. Dev







0

0.9732

1.2527

1.8032

2.0923

0.44

id="TIG0"

k1_bondorder1

[*:1]~[#6X3:2]~[#6X3:3]~[*:4

1

4.1154

3.5798

2.8599

2.5750

0.60



k1_bondorder2

[*:1]~[#6X3:2]~[#6X3:3]~[*:4

2

0.9954

1.0123

1.0206

1.0237

0.01

id="TIG3"

k1_bondorder1

[#6X3:1]~[#6X3:2]~[#6X3:3]~[*:4

3

3.2039

3.8387

4.0709

4.1598

0.37



k1_bondorder2

[#6X3:1]~[#6X3:2]~[#6X3:3]~[*:4

4

1.0432

1.0604

1.0674

1.0705

0.01

id="TIG4"

k1_bondorder1

[#7X2:1]@[#6X3:2]~[#6X3:3]@[*:4

5

5.6374

6.5924

8.1392

9.0236

1.32



k1_bondorder2

[#7X2:1]@[#6X3:2]~[#6X3:3]@[*:4

6

2.5752

2.5628

2.3147

2.2081

0.16

id="TIG5a"

k1_bondorder1

[#7X3,#8X2,#16X2:1]~[#6X3:2]~[#6X3:3](=[#8X1])~[*:4

7

7.9449

6.4655

4.3205

3.3987

1.78



k1_bondorder2

[#7X3,#8X2,#16X2:1]~[#6X3:2]~[#6X3:3](=[#8X1])~[*:4

8

0.8864

0.8631

0.8316

0.8184

0.03

id="TIG5b"

k1_bondorder1

[#7X3,#8X2,#16X2:1]@[#6X3:2]~[#6X3:3]@[*:4

9

6.5726

4.9785

-0.0706

-2.6145

3.71



k1_bondorder2

[#7X3,#8X2,#16X2:1]@[#6X3:2]~[#6X3:3]@[*:4

10

1.6884

1.8019

1.8660

1.8933

0.08

id="TIG1c"

k1_bondorder1

[*:1]~[#6X3:2](=[#8X1,#16X1])~[#7X3,#7X2-1:3]~[*:4

11

6.7638

5.6549

3.9703

3.2175

1.39



k1_bondorder2

[*:1]~[#6X3:2](=[#8X1,#16X1])~[#7X3,#7X2-1:3]~[*:4

12

1.1548

1.1489

1.1463

1.1478

0.00

id="TIG6"

k1_bondorder1

[#6X3:1]~[#6X3:2]~[#7X3,#7X2-1:3]~[*:4

13

3.0805

3.3722

3.3737

3.3445

0.12



k1_bondorder2

[#6X3:1]~[#6X3:2]~[#7X3,#7X2-1:3]~[*:4

14

1.2382

1.3251

1.3139

1.3109

0.03

id="TIG7"

k1_bondorder1

[#7X2:1]~[#6X3:2]~[#7X3,#7X2-1:3]~[*:4

15

10.2940

10.9290

11.6510

11.9470

0.64



k1_bondorder2

[#7X2:1]~[#6X3:2]~[#7X3,#7X2-1:3]~[*:4

16

1.0027

1.0493

1.0512

1.0443

0.02

id="TIG8"

k1_bondorder1

[#7X3,#8X2,#16X2:1]@[#6X3:2]~[#7X3,#7X2-1:3]~[*:4

17

9.5042

9.5360

9.6940

9.9457

0.17



k1_bondorder2

[#7X3,#8X2,#16X2:1]@[#6X3:2]~[#7X3,#7X2-1:3]~[*:4

18

1.3948

1.4833

1.5130

1.5212

0.05

id="TIG2"

k1_bondorder1

[*:1]~[#6X3:2]~[#7X2,#7X3+1:3]~[*:4

19

5.3789

6.4891

6.8710

7.0001

0.64



k1_bondorder2

[*:1]~[#6X3:2]~[#7X2,#7X3+1:3]~[*:4

20

1.5231

1.4808

1.4835

1.4873

0.02

id="TIG1d"

k1_bondorder1

[*:1]~[#6X3:2](~[#7X2])~[#7X3,#7X2-1,#7X2,#7X3+1:3]~[*:4

21

8.1257

8.3387

8.1386

7.9966

0.12



k1_bondorder2

[*:1]~[#6X3:2](~[#7X2])~[#7X3,#7X2-1,#7X2,#7X3+1:3]~[*:4

 

The table below is with an already optimized fit (with prior=2) as a starting point.

Fit 7

Prior = 2

Prior = 0.2

Prior = 5

Prior = 10







Obj. fn value (X2)

1547.05

1544.52

1539.64

1537.61























0

1.2527

1.2527

1.9039

2.1254

id="TIG0"

k1_bondorder1

[*:1]~[#6X3:2]~[#6X3:3]~[*:4]

1

3.5798

3.5798

2.7207

2.5337



k1_bondorder2

[*:1]~[#6X3:2]~[#6X3:3]~[*:4]

2

1.0123

1.0123

1.0219

1.0240

id="TIG3"

k1_bondorder1

[#6X3:1]~[#6X3:2]~[#6X3:3]~[*:4]

3

3.8387

3.8387

4.1141

4.1722



k1_bondorder2

[#6X3:1]~[#6X3:2]~[#6X3:3]~[*:4]

4

1.0604

1.0604

1.0689

1.0709

id="TIG4"

k1_bondorder1

[#7X2:1]@[#6X3:2]~[#6X3:3]@[*:4]

5

6.5924

6.5924

8.4504

9.1038



k1_bondorder2

[#7X2:1]@[#6X3:2]~[#6X3:3]@[*:4]

6

2.5628

2.5629

2.2679

2.1932

id="TIG5a"

k1_bondorder1

[#7X3,#8X2,#16X2:1]~[#6X3:2]~[#6X3:3](=[#8X1])~[*:4]

7

6.4655

6.4655

3.9102

3.2698



k1_bondorder2

[#7X3,#8X2,#16X2:1]~[#6X3:2]~[#6X3:3](=[#8X1])~[*:4]

8

0.8631

0.8631

0.8270

0.8177

id="TIG5b"

k1_bondorder1

[#7X3,#8X2,#16X2:1]@[#6X3:2]~[#6X3:3]@[*:4]

9

4.9785

4.9785

-0.8443

-2.7424



k1_bondorder2

[#7X3,#8X2,#16X2:1]@[#6X3:2]~[#6X3:3]@[*:4]

10

1.8019

1.8019

1.8771

1.8973

id="TIG1c"

k1_bondorder1

[*:1]~[#6X3:2](=[#8X1,#16X1])~[#7X3,#7X2-1:3]~[*:4]

11

5.6549

5.6549

3.6566

3.1130



k1_bondorder2

[*:1]~[#6X3:2](=[#8X1,#16X1])~[#7X3,#7X2-1:3]~[*:4]

12

1.1489

1.1491

1.1460

1.1477

id="TIG6"

k1_bondorder1

[#6X3:1]~[#6X3:2]~[#7X3,#7X2-1:3]~[*:4]

13

3.3722

3.3724

3.3763

3.3458



k1_bondorder2

[#6X3:1]~[#6X3:2]~[#7X3,#7X2-1:3]~[*:4]

14

1.3251

1.3251

1.3129

1.3104

id="TIG7"

k1_bondorder1

[#7X2:1]~[#6X3:2]~[#7X3,#7X2-1:3]~[*:4]

15

10.9290

10.9290

11.7830

11.9870



k1_bondorder2

[#7X2:1]~[#6X3:2]~[#7X3,#7X2-1:3]~[*:4]

16

1.0493

1.0493

1.0505

1.0443

id="TIG8"

k1_bondorder1

[#7X3,#8X2,#16X2:1]@[#6X3:2]~[#7X3,#7X2-1:3]~[*:4]

17

9.5360

9.5360

9.7187

9.9817



k1_bondorder2

[#7X3,#8X2,#16X2:1]@[#6X3:2]~[#7X3,#7X2-1:3]~[*:4]

18

1.4833

1.4833

1.5183

1.5220

id="TIG2"

k1_bondorder1

[*:1]~[#6X3:2]~[#7X2,#7X3+1:3]~[*:4]

19

6.4891

6.4891

6.9427

7.0142



k1_bondorder2

[*:1]~[#6X3:2]~[#7X2,#7X3+1:3]~[*:4]

20

1.4808

1.4808

1.4836

1.4875

id="TIG1d"

k1_bondorder1

[*:1]~[#6X3:2](~[#7X2])~[#7X3,#7X2-1,#7X2,#7X3+1:3]~[*:4]

21

8.3387

8.3387

8.1015

7.9836



k1_bondorder2

[*:1]~[#6X3:2](~[#7X2])~[#7X3,#7X2-1,#7X2,#7X3+1:3]~[*:4]