Physics‐Informed Deep Learning Method for Real‐Time Multi‐Harmonic Beamforming Based on Space‐Time‐Coding Metasurface

ABSTRACT Space‐time‐coding metasurfaces (STCMs) enable simultaneous controls of electromagnetic wave across multiple harmonics, but designing high‐performance coding sequences in real time remains challenging. Here, we propose an unsupervised physics‐informed deep learning framework that can generate optimal spatiotemporal coding patterns for arbitrary single‐ and dual‐beam requirements at each harmonic frequency. The proposed method features three key innovations: physics‐informed mechanisms to enable unsupervised learning without requiring paired training data, a dedicated strategy for multi‐bit metasurface configurations, and the Conflict Averse Gradient descent (CAGrad) method to coordinate the parameter optimization across harmonics in multi‐task learning. Experiments on a 2‐bit STCM demonstrate robust beamforming capabilities over five harmonics, achieving an average radiation difference of 1.55 dB and real‐time design <0.1s. This is a 4‐order‐of‐magnitude improvement in computational efficiency compared with the particle swarm optimization methods. This work establishes a real‐time and physics‐aware design paradigm for intelligent metasurfaces in the next‐generation wireless systems.