Exploring the Nonlinear Relationships Between Oceanic Indices Using Quantum and Classical Machine Learning Approaches

Understanding the complex interrelationships between oceanic climate indices such as the Indian Ocean Dipole (IOD), El Niño–Southern Oscillation (ENSO), Arctic Oscillation (AO), and Atlantic Multidecadal Oscillation (AMO) is crucial for improving long-term climate predictions. However, traditional linear models often fail to capture the intricate, nonlinear dependencies that govern these systems. As a result, these models struggle to accurately predict key oceanic anomalies and associated climatic events, such as tropical cyclones that significantly impact India and its surrounding regions. In this study, we investigate both classical and quantum machine learning approaches to analyze the nonlinear interconnections among the four major oceanic indices. Using Random Forests and Mutual Information, we identify influencing relationships beyond what is revealed by linear correlation. To enhance interpretability and model generalization, we employ symbolic regression (via PySR) to derive analytical expressions that define the interactions among the indices. Our findings reveal hidden nonlinear influences—particularly highlighting that while AMO appears to have minimal effect under linear analysis, it plays a more subtle but critical role in the broader climate system. By combining symbolic and quantum machine learning techniques, this research offers a novel, interpretable framework for understanding complex ocean-atmosphere dynamics and lays the groundwork for improved forecasting of extreme weather events such as tropical cyclones in the Indian subcontinent