Physics-Informed Neural Networks (PINN) for temporal forecasting of monsoon rainfall variability in southern peninsular India

Rainfall significantly influences the climatic and hydrological systems of Southern Peninsular India, a region known for its intricate weather dynamics and reliance on monsoon rainfall. This study introduces a dual-methodology framework combining Exploratory Data Analysis (EDA) with a Physics-Informed Neural Network (PINN) to explore rainfall variability effectively. EDA is employed as an essential tool to derive insights from historical precipitation datasets through statistical analysis, enabling the identification of patterns, anomalies, and trends. To complement this statistical groundwork, a novel PINN model is developed, leveraging principles from Bernoulli's equation to enhance the learning process to forecast rainfall for five states of southern peninsula of India viz., Coastal Andra, Coastal Karnataka, Kerala, Tamil Nadu, Telangana. By mapping the loss gradient to pressure changes, momentum to kinetic energy, and regularization to potential energy, the PINN framework mirrors the principles of conservation and fluid dynamics, ensuring robust and efficient training convergence in neural networks. The model also incorporates innovative techniques, including a Convergence Weight Index (WCI) and adaptive weight updates guided by the rate of loss reduction, to improve training stability and prevent overfitting. Additionally, advancements in PINN methodologies, such as multi-task optimization, modular decomposition of large datasets, and integration with hybrid architectures, are utilized to address the challenges of noisy and nonlinear precipitation data. This study makes key contributions by providing a EDA and machine learning techniques, proposing a Bernoulli-inspired PINN for precipitation modeling, and introducing novel mechanisms to enhance predictive performance. The findings underscore the utility of physics-augmented machine learning models in analysing complex environmental systems like rainfall variability.