Oscillatory neural networks (ONNs) represent a neuromorphic computing paradigm that leverages the phase dynamics of coupled oscillators to encode and process information [1]. A vanadium dioxide (VO₂) oscillator network is a specific type of neuromorphic architecture that utilizes the phase transition properties of VO₂ to create oscillating neurons interconnected with resistive or capacitive components. Coupling elements based on resistive random-access memory (ReRAM) enable programmable and trainable network connectivity [2]. These circuits are being explored for applications such as associative memory and pattern recognition [3], where the network's ability to synchronize in phase and frequency is utilized. Additionally, oscillation-based computing is highly effective for solving complex optimization problems (COPs), which typically require extensive computing resources, long processing times, and significant energy consumption [4].

In this work, we explore ONNs based on VO₂ oscillators and HfO₂-based analog ReRAM. The fabrication processes for both types of devices have been optimized to be back-end-of-line (BEOL) compatible, allowing for post-processing on top of an underlying CMOS circuit [5]. Regular VO₂ undergoes a reversible insulator-to-metal transition (IMT) at approximately 68°C, which can be increased by 20°C or more through doping or alloying. VO₂ devices excel in scalability and low power consumption due to their crossbar geometry, and they demonstrate long endurance of more than 10¹² cycles. The ReRAM devices used in this work consist of a conductive metal oxide (CMO) and a dielectric HfO_x, stacked between TiN electrodes. Their programmable multilevel resistance states make them ideal candidates for trainable ONNs.

We have demonstrated applications such as pattern or image recognition and COP tasks with VO₂ ONNs. Specifically, we have solved fundamental optimization problems like Graph Coloring, Max-cut, and Max-3SAT. By leveraging the natural tendency of oscillators to stabilize into defined state relationships, we achieve solution convergence within fewer than 25 oscillation cycles, a significantly faster process than traditional computers testing all possible combinations. We successfully mapped graph problems to ONNs with 9 VO₂ oscillators, attaining optimal solutions with high probability. The integration of VO₂ oscillators and HfO₂ ReRAM coupling arrays enables flexible re-programming of ONNs using the switching capability of ReRAM. The multi-level resistance tuning of our ReRAM allows fine adjustment of the coupling strength between individual oscillators in the ONN.