Table 3.

The AI algorithms used for the prediction of mechanical metamaterials properties and their inverse design

AI algorithms	Advantages	Disadvantages	Prediction		Inverse design
			Type	Ref.	Type	Ref.
Artificial neural networks	• Flexibility and scalability • Computationally efficient • Parallel processing • Powerful ability to extract features in data	• Accuracy relies on amount of data • Prone to overfitting • Black box nature	Nonlinear mechanical metamaterials and fractal metamaterials	157,193	Inflatable soft membranes	158
Deep learninga	• Powerful ability to extract features in data • Handling complex Data • Parallel processing • Flexibility and scalability	• Computationally intensive • Accuracy relies on large amount of image data • Prone to overfitting • Black box nature	Copper spheres embedded in polylactide matrices	194	2D and elastic mechanical metamaterials	153,195
			Tetra-chiral auxetics, cellular metamaterials	196,197	Gradient mechanical metamaterials	155,198
			Magneto-mechanical metamaterials and auxetic kirigami metamaterials	199,200	Metasurfaces, magneto-mechanical metamaterials and auxetic mechanical metamaterials	154,199,201
Evolutionary strategyb	• Exceling at global optimization • Scalability and invariance • Built-in feature selection • High interpretability • Robustness to noise • Less susceptible to overfitting	• Computationally intensive • Fixed standard deviation parameter of noise • Slow search speed	Nanoscale corrugated plates	202	2D and 3D mechanical metamaterial with nonlinear response, fractal metamaterials	157,193,203
Genetic programming	• Global search ability • Scalability • Simple process • Built-in feature selection • High interpretability • Robustness to noise	• Computationally intensive • Complicated programming implementation • Slow search speed	Graphene origami metamaterials	204,205	Auxetic mechanical metamaterials with zero Poisson’s ratio	206
Bayesian network classifiers	• High learning efficiency • Small time and space overhead in classification	• Computational complexity • Dimensional challenges in computing probability • Low interpretability	--	--	Mechanical metamaterials with negative stiffness	151
Decision trees	• Simple data preparation • High interpretability • High efficiency and accuracy	• Prone to overfitting • Bias toward features with more levels • Difficulty in handling missing data	Non-rigid square-twist origami	207	--	--

^aDeep learning is a specialization of artificial neural networks with multiple hidden layers.

^bEvolutionary strategy and genetic programming are branches of evolutionary computation.