Table 6 Polynomial and fourier expansion inspired augmentation results on all the 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

1931.3746

43.94741

27.46238

0.99699

0.00736

0.7344

178

Random Forest + LR

0.9977

1469.6999

38.33666

23.45429

0.99771

0.00619

0.61692

177.99946

kNN + LR

0.99785

1372.5477

37.04791

23.55665

0.99786

0.00617

0.61853

122

LightGBM

0.98318

10781.187

103.83249

28.65942

0.9832

0.00878

0.81655

1521.0977

Gradient Boosting + LR

0.99472

3380.0522

58.13821

42.25681

0.99472

0.01171

1.16962

340.01416

AdaBoost + LR

0.92916

45403.068

213.07995

147.83869

0.92933

0.04052

3.94398

1370.6301

CatBoost

0.99896

665.76746

25.80247

14.65029

0.99896

0.004

0.40035

128.18601

XGBoost

0.99844

998.57142

31.60018

18.35327

0.99845

0.00485

0.48388

171.73657

MLP + LR

0.99860

894.58980

29.90969

20.14475

0.99860

0.00527

0.52620

109.22297

GRU

0.99901

631.57643

25.13118

16.58329

0.99915

0.00443

0.44334

114.03687

LSTM + LR

0.99884

740.51274

27.21236

17.0143

0.99885

0.00456

0.456

177.3122

Autoencoders + LR

0.99853

940.02177

30.65977

18.22995

0.99853

0.00508

0.5083

198.1172