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Abstract In recent years, wave-based analog computing has been at the center of attention for providing ultra-fast and power-efficient signal processing enabled by wave propagation through artificially engineered structures. Building on these structures, various proposals have been put forward for performing computations with waves. Most of these proposals have been aimed at linear operations, such as vector-matrix multiplications. The weak and hardly controllable nonlinear response of electromagnetic materials imposes challenges in the design of wave-based structures for performing nonlinear operations. In the present work, first, by using the method of inverse design we propose a three-port device, which consists of a combination of linear and Kerr nonlinear materials, exhibiting the desired power-dependent transmission properties. Then, combining a proper arrangement of such devices with a collection of Mach–Zehnder interferometers (MZIs), we propose a reconfigurable nonlinear optical architecture capable of implementing a variety of nonlinear functions of the input signal. The proposed device may pave the way for wave-based reconfigurable nonlinear signal processing that can be combined with linear networks for full-fledged wave-based analog computing.