Creation of a computational space with model-free metasurface neural network

Physical neural networks (PNNs) are neural-like computational frameworks that exploit the intrinsic dynamics of physical media to achieve ultrafast and energy-efficient information processing. However, the complex and strongly-coupled physical nature of PNNs in disordered environments makes them resistant to accurate differentiable modeling. Here, we propose a concept of computational space that empowers the chaotic environment itself with computational capabilities. This space constitutes a large-scale, model-agnostic PNN through distributed intelligent metasurfaces. To enable effective training, we develop a fully-forward learning framework that estimates zeroth-order gradients from in-situ measurable electromagnetic feedback, thereby circumventing the rigorous modeling requirements of conventional backpropagation. In experiments, we construct such computational space that achieves recognition accuracies of 97% for alphabetic characters and 99% for numeric patterns. Furthermore, the space exhibits the functionalities of enhanced focusing under disordered scattering conditions and reliable human position localization. This emerging paradigm of self-evolving physical intelligence holds potential for advancing embodied intelligence, autonomous cyber-physical systems, and next-generation human-machine interaction, marking a fundamental transition from computing the physics to computing with physics.