Fig. 1. Classification of deep learning-based electromagnetic metamaterial design methods. Deep learning (DL)-assisted methods use traditional algorithms as optimization solvers, and simulation data associated with a specific structural configuration as training set^[47]. Direct DL design predicts structures from targets using networks like tandem or generative ones, needing a dataset of optimized solutions^[48]. Physics-informed neural networks (PINN) integrate physical laws, using PDE data, BCs/ICs, and PDE residual to solve equations without simulation data^[49]

Fig. 2. Inverse design of electromagnetic metamaterials based on deep learning-assisted methods. (a) Architecture of neural network used to predict optical response of metasurface structure^[47]; (b) schematic of deep neural network structure^[50]; (c) schematic of 101-layer deep residual network architecture^[51]; (d) flowchart of co-evolution algorithm^[52]; (e) schematic of transfer learning for real-part spectrum of rectangular meta-atoms^[53]; (f) schematic of conditional GLOnet used for generative aggregation^[57]

Fig. 3. Feedforward neural network for direct design. (a) Schematic of overall scheme for inverse design of a visible light band filter^[68]; (b) diagram of metasurface design based on tandem neural networks and iterative algorithms^[69]; (c) architecture diagram of generative network when traditional trial-and-error method is transformed into neural network-mediated inverse design^[48]; (d) schematic of training scheme, and the initial training set includes high-performance devices for sparse sampling of device parameter space^[71]

Fig. 4. Direct design of sequence model networks. (a) Schematic diagram of MST network framework for SMA design^[72]; (b) schematic diagram of all-dielectric SERS metasurface design framework based on quasi-continuous spectral states^[73]; (c) schematic diagram of divide-and-conquer deep learning architecture for direct and inverse design applied to terahertz fingerprint sensing^[74]; (d) divide-and-conquer deep learning architecture based on bidirectional artificial neural networks^[75]

Fig. 5. Inverse design of electromagnetic metamaterials based on PINN. (a) Schematic of general PINN building blocks, consisting of a neural network, a PINN, and a feedback mechanism, where PINN is composed of residual terms from differential equations, initial conditions, and boundary conditions^[46]; (b) diagram of PINN used for solving photonic inverse problems based on PDE^[44]; (c) schematic of the network from a single dataset with initial/boundary conditions (I/BC)^[78]; (d) diagram of deep Lorentz neural network^[82]