Asian Journal of Pure and Applied Mathematics

Geological hazards including landslides, earthquakes, volcanic eruptions, and floods—pose significant risks to human societies, infrastructure, and ecosystems. Reliable prediction and risk assessment are essential for effective disaster mitigation and resilience planning. Conventional approaches, such as empirical methods and physics-based simulations, often face limitations in capturing the complex, nonlinear, and multi-scale behavior of geological systems. Recent advances in deep learning and partial differential equation (PDE)-based modeling offer promising alternatives to address these challenges.

Deep learning techniques, including convolutional neural networks (CNNs) and recurrent neural networks (RNNs), can extract complex spatial and temporal patterns from large-scale datasets such as seismic records, satellite imagery, and in situ sensor measurements. In parallel, PDE-based models provide physics-informed representations of geological processes by describing system evolution under governing physical laws and boundary conditions. Integrating these methodologies has led to hybrid frameworks, such as physics-informed neural networks (PINNs) and coupled PDE–deep learning models, which combine data-driven adaptability with physical consistency and improved generalization.

This review summarizes state-of-the-art applications in landslide susceptibility mapping, seismic hazard assessment, and flood prediction. It also discusses key challenges, including data quality and heterogeneity, model transferability across regions, uncertainty quantification, and computational demands. Case studies demonstrate that integrated modeling approaches enhance predictive accuracy and support real-time early warning systems. Future research directions include multi-hazard modeling, integration with Internet of Things (IoT) sensor networks, and scalable real-time monitoring frameworks to advance predictive geoscience and disaster resilience.