Table 3 Results of direct implementation of predictive Models.

From: Comprehensive framework of machine learning and deep learning architectures with metaheuristic optimization for high-fidelity prediction of nanofluid specific heat capacity

Final Models

\(\:{\varvec{R}}^{2}\) Score

MSE

RMSE

MAE

EVS

MAPE

SMAPE

Max Error

Decision Tree

0.99699

1926.219

43.88872

27.33363

0.99701

0.00733

0.73071

178

Random Forest + LR

0.99729

1734.260

41.64445

23.72606

0.9973

0.00661

0.65524

311.23768

kNN + LR

0.99252

4792.8369

69.23032

30.4877

0.99252

0.00924

0.89398

691.48382

LightGBM

0.95415

29386.438

171.42473

79.29507

0.95420

0.02117

2.05022

1008.3917

Gradient Boosting + LR

0.99471

3389.8957

58.22281

42.34641

0.99471

0.01175

1.17329

340.01416

AdaBoost + LR

0.94458

35517.396

188.46059

148.06786

0.94485

0.03955

3.93416

626.4249

CatBoost

0.99876

791.07331

28.12602

16.99067

0.99876

0.00458

0.45613

182.87230

XGBoost

0.99893

681.92540

26.11370

16.95128

0.99893

0.00455

0.45442

121.06347

MLP + LR

0.99786

1370.7032

37.02300

21.20976

0.99786

0.00569

0.57347

331.81693

GRU

0.99826

1113.1856

33.36444

22.83463

0.99842

0.00596

0.59937

174.52637

LSTM + LR

0.99857

917.79771

30.29518

22.05073

0.99857

0.00596

0.59515

104.54755

Autoencoders + LR

0.99921

509.21466

22.56579

13.29329

0.99921

0.00356

0.35602

114.69256