Solving Sudoku using oscillatory neural networks

We explore the capabilities of physical computing with Oscillatory Neural Networks (ONN) to solve combinatorial optimization problems. To solve Sudokus with ONNs, we define a novel mapping strategy that utilizes the unique characteristics of the computation paradigm. The problem is encoded through a puzzle specific graph-embedding, which implements the constraints through different subgraphs. These subgraphs are then combined into a single adjacency matrix, which allows the natural dynamics of the phases of coupled oscillators to find a solution to the puzzle. We model the phase dynamics of the ONN by means of the Kuramoto differential equation. This novel approach is then compared to the well-established iterative method to solve Sudoku already used in binary Hopfield networks (HNN). Solving optimization problems typically requires a large amount of energy to solve on conventional hardware. Therefore, we are motivated to explore the mapping of Sudoku from a theoretical point of view to establish the validity of this approach. The simulation results show that the novel ONN mapping outperforms the established HNN methodology.