Nonlinear In-situ Physical Adjoint Computing using Complex Multi-resonant Cavities

We present an algorithm that discovers device and wavefront parameter settings to achieve extreme control of wave propagation in complex scattering networks with local nonlinearities. The method treats the steady-state field as the solution of a nonlinear equation and uses an adjoint field to compute gradients with respect to both structural controls (e.g., cavity couplings) and injected wavefront amplitudes/phases. Crucially, each gradient evaluation requires only two full-field experiments, one forward excitation and one adjoint excitation, enabling fast, scalable, gradient-based optimization across thousands of degrees of freedom without neural-network training or surrogate/Bayesian sweeps. We implement the protocol on a microwave graph platform augmented by a localized, saturable nonlinear resonator, but the formulation is platform-agnostic. Using objective function tailored to desired phenomena, we realize canonical and nonlinear-specific modalities, including coherent perfect absorption, arbitrary power splitting, and asymmetric transport. By unifying forward physics with adjoint sensitivity in nonlinear media, our approach delivers a versatile pathway to rapid, high-fidelity wave control for applications in next-generation communication, wireless power delivery, and physical neural networks.