9.1. How to tune Fitting/embedding-net size ?
Here are some test forms on fitting-net size tuning or embedding-net size tuning performed on several different systems.
9.1.1. Al2O3
9.1.1.1. Fitting net size tuning form on Al2O3: (embedding-net size: [25,50,100])
Fitting-net size |
Energy L2err(eV) |
Energy L2err/Natoms(eV) |
Force L2err(eV/Angstrom) |
---|---|---|---|
[240,240,240] |
1.742252e-02 |
7.259383e-05 |
4.014115e-02 |
[80,80,80] |
1.799349e-02 |
7.497287e-05 |
4.042977e-02 |
[40,40,40] |
1.799036e-02 |
7.495984e-05 |
4.068806e-02 |
[20,20,20] |
1.834032e-02 |
7.641801e-05 |
4.094784e-02 |
[10,10,10] |
1.913058e-02 |
7.971073e-05 |
4.154775e-02 |
[5,5,5] |
1.932914e-02 |
8.053808e-05 |
4.188052e-02 |
[4,4,4] |
1.944832e-02 |
8.103467e-05 |
4.217826e-02 |
[3,3,3] |
2.068631e-02 |
8.619296e-05 |
4.300497e-02 |
[2,2,2] |
2.267962e-02 |
9.449840e-05 |
4.413609e-02 |
[1,1,1] |
2.813596e-02 |
1.172332e-04 |
4.781115e-02 |
[] |
3.135002e-02 |
1.306251e-04 |
5.373120e-02 |
[] means no hidden layer, but there is still a linear output layer. This situation is equal to the linear regression.
9.1.1.2. Embedding net size tuning form on Al2O3: (Fitting-net size: [240,240,240])
Embedding-net size |
Energy L2err(eV) |
Energy L2err/Natoms(eV) |
Force L2err(eV/Angstrom) |
---|---|---|---|
[25,50,100] |
1.742252e-02 |
7.259383e-05 |
4.014115e-02 |
[10,20,40] |
2.909990e-02 |
1.212496e-04 |
4.734667e-02 |
[5,10,20] |
3.357767e-02 |
1.399070e-04 |
5.706385e-02 |
[4,8,16] |
6.060367e-02 |
2.525153e-04 |
7.333304e-02 |
[3,6,12] |
5.656043e-02 |
2.356685e-04 |
7.793539e-02 |
[2,4,8] |
5.277023e-02 |
2.198759e-04 |
7.459995e-02 |
[1,2,4] |
1.302282e-01 |
5.426174e-04 |
9.672238e-02 |
9.1.2. Cu
9.1.2.1. Fitting net size tuning form on Cu: (embedding-net size: [25,50,100])
Fitting-net size |
Energy L2err(eV) |
Energy L2err/Natoms(eV) |
Force L2err(eV/Angstrom) |
---|---|---|---|
[240,240,240] |
4.135548e-02 |
1.615449e-04 |
8.940946e-02 |
[20,20,20] |
4.323858e-02 |
1.689007e-04 |
8.955762e-02 |
[10,10,10] |
4.399364e-02 |
1.718502e-04 |
8.962891e-02 |
[5,5,5] |
4.468404e-02 |
1.745470e-04 |
8.970111e-02 |
[4,4,4] |
4.463580e-02 |
1.743586e-04 |
8.972011e-02 |
[3,3,3] |
4.493758e-02 |
1.755374e-04 |
8.971303e-02 |
[2,2,2] |
4.500736e-02 |
1.758100e-04 |
8.973878e-02 |
[1,1,1] |
4.542073e-02 |
1.774247e-04 |
8.964761e-02 |
[] |
4.545168e-02 |
1.775456e-04 |
8.983201e-02 |
9.1.2.2. Embedding net size tuning form on Cu: (Fitting-net size: [240,240,240])
Embedding-net size |
Energy L2err(eV) |
Energy L2err/Natoms(eV) |
Force L2err(eV/Angstrom) |
---|---|---|---|
[25,50,100] |
4.135548e-02 |
1.615449e-04 |
8.940946e-02 |
[20,40,80] |
4.203562e-02 |
1.642016e-04 |
8.925881e-02 |
[15,30,60] |
4.146672e-02 |
1.619794e-04 |
8.936911e-02 |
[10,20,40] |
4.263060e-02 |
1.665258e-04 |
8.955818e-02 |
[5,10,20] |
4.994913e-02 |
1.951138e-04 |
9.007786e-02 |
[4,8,16] |
1.022157e-01 |
3.992802e-04 |
9.532119e-02 |
[3,9,12] |
1.362098e-01 |
5.320695e-04 |
1.073860e-01 |
[2,4,8] |
7.061800e-02 |
2.758515e-04 |
9.126418e-02 |
[1,2,4] && seed = 1 |
9.843161e-02 |
3.844985e-04 |
9.348505e-02 |
[1,2,4] && seed = 2 |
9.404335e-02 |
3.673568e-04 |
9.304089e-02 |
[1,2,4] && seed = 3 |
1.508016e-01 |
5.890688e-04 |
1.382356e-01 |
[1,2,4] && seed = 4 |
9.686949e-02 |
3.783965e-04 |
9.294820e-02 |
9.1.3. Water
9.1.3.1. Fitting net size tuning form on water: (embedding-net size: [25,50,100])
Fitting-net size |
Energy L2err/Natoms(eV) |
Force L2err(eV/Angstrom) |
---|---|---|
[240,240,240] |
9.1589E-04 |
5.1540E-02 |
[200,200,200] |
9.3221E-04 |
5.2366E-02 |
[160,160,160] |
9.4274E-04 |
5.3403E-02 |
[120,120,120] |
9.5407E-04 |
5.3093E-02 |
[80,80,80] |
9.4605E-04 |
5.3402E-02 |
[40,40,40] |
9.8533E-04 |
5.5790E-02 |
[20,20,20] |
1.0057E-03 |
5.8232E-02 |
[10,10,10] |
1.0466E-03 |
6.2279E-02 |
[5,5,5] |
1.1154E-03 |
6.7994E-02 |
[4,4,4] |
1.1289E-03 |
6.9613E-02 |
[3,3,3] |
1.2368E-03 |
7.9786E-02 |
[2,2,2] |
1.3558E-03 |
9.7042E-02 |
[1,1,1] |
1.4633E-03 |
1.1265E-01 |
[] |
1.5193E-03 |
1.2136E-01 |
9.1.3.2. Embedding net size tuning form on water: (Fitting-net size: [240,240,240])
Embedding-net size |
Energy L2err/Natoms(eV) |
Force L2err(eV/Angstrom) |
---|---|---|
[25,50,100] |
9.1589E-04 |
5.1540E-02 |
[20,40,80] |
9.5080E-04 |
5.3593E-02 |
[15,30,60] |
9.7996E-04 |
5.6338E-02 |
[10,20,40] |
1.0353E-03 |
6.2776E-02 |
[5,10,20] |
1.1254E-03 |
7.3195E-02 |
[4,8,16] |
1.2495E-03 |
8.0371E-02 |
[3,6,12] |
1.3604E-03 |
9.9883E-02 |
[2,4,8] |
1.4358E-03 |
9.7389E-02 |
[1,2,4] |
2.1765E-03 |
1.7276E-01 |
9.1.4. Mg-Al
9.1.4.1. Fitting net size tuning form on Mg-Al: (embedding-net size: [25,50,100])
Fitting-net size |
Energy L2err/Natoms(eV) |
Force L2err(eV/Angstrom) |
---|---|---|
[240,240,240] |
3.9606e-03 |
1.6289e-02 |
[200,200,200] |
3.9449e-03 |
1.6471e-02 |
[160,160,160] |
4.0947e-03 |
1.6413e-02 |
[120,120,120] |
3.9234e-03 |
1.6283e-02 |
[80,80,80] |
3.9758e-03 |
1.6506e-02 |
[40,40,40] |
3.9142e-03 |
1.6348e-02 |
[20,20,20] |
4.1302e-03 |
1.7006e-02 |
[10,10,10] |
4.3433e-03 |
1.7524e-02 |
[5,5,5] |
5.3154e-03 |
1.9716e-02 |
[4,4,4] |
5.4210e-03 |
1.9710e-02 |
[2,2,2] |
6.2667e-03 |
2.2568e-02 |
[1,1,1] |
7.3676e-03 |
2.6375e-02 |
[] |
7.3999e-03 |
2.6097e-02 |
9.1.4.2. Embedding net size tuning form on Mg-Al: (Fitting-net size: [240,240,240])
Embedding-net size |
Energy L2err/Natoms(eV) |
Force L2err(eV/Angstrom) |
---|---|---|
[25,50,100] |
3.9606e-03 |
1.6289e-02 |
[20,40,80] |
4.0292e-03 |
1.6555e-02 |
[15,30,60] |
4.1743e-03 |
1.7026e-02 |
[10,20,40] |
4.8138e-03 |
1.8516e-02 |
[5,10,20] |
5.6052e-03 |
2.0709e-02 |
[4,8,16] |
6.1335e-03 |
2.1450e-02 |
[3,6,12] |
6.6469e-03 |
2.3003e-02 |
[2,4,8] |
6.8222e-03 |
2.6318e-02 |
[1,2,4] |
1.0678e-02 |
3.9559e-02 |