  Reconfigurable intelligent surface (RIS) has become a promising technology to
realize the programmable wireless environment via steering the incident signal
in fully customizable ways. However, a major challenge in RIS-aided
communication systems is the simultaneous design of the precoding matrix at the
base station (BS) and the phase shifting matrix of the RIS elements. This is
mainly attributed to the highly non-convex optimization space of variables at
both the BS and the RIS, and the diversity of communication environments.
Generally, traditional optimization methods for this problem suffer from the
high complexity, while existing deep learning based methods are lack of
robustness in various scenarios. To address these issues, we introduce a
gradient-based manifold meta learning method (GMML), which works without
pre-training and has strong robustness for RIS-aided communications.
Specifically, the proposed method fuses meta learning and manifold learning to
improve the overall spectral efficiency, and reduce the overhead of the
high-dimensional signal process. Unlike traditional deep learning based methods
which directly take channel state information as input, GMML feeds the
gradients of the precoding matrix and phase shifting matrix into neural
networks. Coherently, we design a differential regulator to constrain the phase
shifting matrix of the RIS. Numerical results show that the proposed GMML can
improve the spectral efficiency by up to 7.31\%, and speed up the convergence
by 23 times faster compared to traditional approaches. Moreover, they also
demonstrate remarkable robustness and adaptability in dynamic settings.
