In-situ Adjoint Wave Control in Reconfigurable Non-Hermitian Nonlinear Systems

Complex multipath environments are usually avoided in wave-based information processing because repeated scattering creates many interfering propagation paths, obscuring controllability and generating extreme sensitivity to perturbations. The addition of nonlinear mechanisms fundamentally alters the wave-control landscape by breaking the superposition principle that underpins most wave-management strategies. Here, we show that these two apparent impediments -- multipath complexity and nonlinearity -- can instead be harnessed as key resources for physical optimization. We demonstrate an in-situ adjoint optimization protocol in a wave-chaotic platform incorporating a single localized nonlinear defect, in which the system itself performs both the forward and the adjoint propagations required for gradient evaluation. Recurrent multipath returns repeatedly expose the wave to the defect, producing from a minimal hardware a rich nonlinear input-output map with many pathway-mediated degrees of freedom. At the same time, a suitable adjoint excitation enables direct extraction of the sensitivities from measurements alone, without a digital twin or conventional numerical backpropagation. We experimentally validate the protocol on a minimal nonlinear multipath platform composed of incommensurate coaxial cables connected via T-junctions, one of which hosts a diode-loaded cavity. Our approach opens a route to adaptive wireless communications, imaging and analog intelligence in complex, partially unknown environments where conventional modeling is impractical.