Detecting high-order rogue waves in two-component Bose–Einstein condensates via a convolutional neural network-based framework

Deep learning has successfully enabled the identification of first-order rogue waves in single-component Bose–Einstein condensates. However, the prediction of rogue waves and identification of high-order rogue waves in two-component coupled Bose–Einstein condensates remain unresolved challenges. In this paper, we extend the application of deep convolutional neural network to the detection of high-order rogue waves in two-component coupled Bose–Einstein condensates by interpreting the spatiotemporal evolution of wave functions as image data. The method successfully learns the complex dynamic behaviors of rogue waves in two-component coupled Bose–Einstein condensates governed by multiple parameters. Moreover, we efficiently locate a narrow, irregular region within the three-dimensional parameter space where second-order-like rogue waves arise. Compared with the tedious iterative processes of numerical methods, this approach significantly reduces computational time—a critical advantage given that time grows exponentially with the number of control parameters. This work provides a scalable tool for exploring complex behaviors in high-dimensional parameter spaces, with potential applications in nonlinear optics, plasma physics, and ocean engineering, where the rapid prediction of extreme waves is critical.