13.1. 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.
13.1.1. Al2O3#
13.1.1.1. 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.
13.1.1.2. 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 |
13.1.2. Cu#
13.1.2.1. 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 |
13.1.2.2. 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 |
[3,6,12] | 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 |
13.1.3. Water#
13.1.3.1. 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 |
13.1.3.2. 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 |
13.1.4. Mg-Al#
13.1.4.1. 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 |
13.1.4.2. 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 |