Table 2 Average mean absolute errors (MAEs) in the test sets for different combinations of target property, model and featurization. Hyperparameter optimization was used throughout with nested 5-fold cross validation. The test MAEs are averaged over 20 test sets using shuffle split with 80/20 splitting. The properties are density, heat of formation of the solid, explosive energy, shock velocity, particle velocity, sound velocity, detonation pressure, detonation temperature, and TNT equivalent per cubic centimeter. The models are kernel ridge regression (KRR), ridge regression (Ridge), support vector regression (SVR), random forest (RF), k-nearest neighbors (kNN), and a take-the-mean dummy predictor. The last row gives the average value for each property in the dataset.

From: Applying machine learning techniques to predict the properties of energetic materials

  \({\boldsymbol{\rho }},\frac{{\bf{g}}}{{\bf{cc}}}\) \({\boldsymbol{\Delta }}{{\boldsymbol{H}}}_{{\boldsymbol{f}}}^{{\boldsymbol{s}}},\frac{{\bf{kJ}}}{{\bf{mol}}}\) \({{\boldsymbol{E}}}_{{\bf{e}}},\frac{{\bf{kJ}}}{{\bf{cc}}}\) \({{\boldsymbol{V}}}_{{\rm{s}}},\frac{{\bf{km}}}{{\bf{s}}}\) \({{\boldsymbol{V}}}_{{\boldsymbol{p}}},\frac{{\bf{km}}}{{\bf{s}}}\) \({{\boldsymbol{V}}}_{{\bf{snd}}},\frac{{\bf{km}}}{{\bf{s}}}\) P, GPa T, K \(\frac{{\bf{TN}}{{\bf{T}}}_{{\bf{equiv}}}}{{\bf{cc}}}\)
KRR Estate 0.10 261.02 0.63 0.48 0.13 0.41 4.95 500.19 0.18
CDS 0.08 198.81 0.50 0.44 0.11 0.37 3.07 462.63 0.17
SoB 0.07 68.73 0.40 0.31 0.09 0.25 2.90 331.36 0.11
CM eigs 0.09 288.41 0.67 0.67 0.18 0.61 5.67 600.08 0.22
Bag of Bonds 0.06 166.66 0.47 0.33 0.11 0.29 3.38 478.93 0.18
Estate + CDS + SoB 0.06 71.40 0.36 0.32 0.10 0.29 2.76 359.66 0.13
Ridge Estate 0.09 269.11 0.58 0.57 0.14 0.45 4.71 491.21 0.19
CDS 0.07 193.19 0.43 0.39 0.11 0.33 3.23 438.27 0.17
SoB 0.06 82.00 0.37 0.32 0.10 0.29 3.01 327.43 0.11
CM eigs 0.09 355.12 0.79 0.60 0.16 0.55 5.82 590.69 0.19
Bag of Bonds 0.06 163.76 0.48 0.32 0.11 0.31 3.37 472.93 0.19
Estate + CDS + SoB 0.06 77.31 0.39 0.32 0.10 0.28 2.78 383.07 0.13
SVR Estate 0.09 207.78 0.60 0.45 0.13 0.35 4.41 476.06 0.17
CDS 0.07 223.24 0.52 0.34 0.12 0.32 3.21 436.81 0.18
SoB 0.06 130.78 0.40 0.31 0.10 0.28 2.97 331.27 0.14
CM eigs 0.08 288.41 0.55 0.60 0.15 0.53 4.54 584.44 0.21
Bag of Bonds 0.07 159.24 0.47 0.35 0.12 0.28 3.34 385.59 0.18
Estate + CDS + SoB 0.06 129.89 0.37 0.34 0.10 0.28 2.73 353.18 0.13
RF Estate 0.09 252.74 0.59 0.50 0.14 0.39 4.09 488.98 0.19
CDS 0.07 241.67 0.46 0.36 0.11 0.29 3.34 435.77 0.16
SoB 0.07 136.91 0.48 0.40 0.12 0.30 3.47 417.46 0.15
CM eigs 0.09 286.89 0.67 0.62 0.15 0.51 5.52 512.22 0.20
Bag of Bonds 0.07 172.41 0.46 0.36 0.10 0.29 3.10 418.35 0.16
Estate + CDS + SoB 0.07 144.18 0.43 0.34 0.09 0.26 3.11 401.27 0.15
kNN Estate 0.08 236.55 0.61 0.49 0.15 0.41 4.30 563.89 0.20
CDS 0.07 242.99 0.55 0.39 0.13 0.33 3.56 478.50 0.18
SoB 0.08 184.43 0.54 0.44 0.12 0.36 3.65 427.20 0.17
CM eigs 0.10 343.48 0.62 0.67 0.15 0.51 5.52 570.55 0.22
Bag of Bonds 0.08 238.05 0.53 0.40 0.11 0.32 3.58 515.25 0.19
Estate + CDS + SoB 0.08 171.65 0.54 0.43 0.12 0.35 3.57 442.14 0.17
mean n/a 0.11 309.75 0.69 0.65 0.15 0.55 4.88 629.20 0.22
  1.86 0.50 3.93 8.47 2.04 6.43 32.13 3568.65 1.43