Flexible RISs: Learning-based Array Manifold Estimation and Phase-shift Optimization

Reconfigurable intelligent surfaces (RISs) are envisioned as a key enabler for next-generation wireless networks, offering programmable control over propagation environments. While extensive research focuses on planar RIS architectures, practical deployments often involve non-planar surfaces, such as structural columns or curved facades, where standard planar beamforming models fail. Moreover, existing analytical solutions for curved RISs are often restricted to specific, pre-defined array manifold geometries. To address this limitation, this paper proposes a novel deep learning (DL) framework for optimizing the phase shifts of non-planar RISs. We first introduce a low-dimensional parametric model to capture arbitrary surface curvature effectively. Based on this, we design a neural network (NN) that utilizes a sparse set of received power measurements to estimate the surface geometry and derive the optimal phase configuration. Simulation results demonstrate that the proposed algorithm converges fast and significantly outperforms conventional planar beamforming designs, validating its robustness against arbitrary surface curvature. We also analyze the impact of the measurement location error on the algorithm's performance.