LE-PDE++: Mamba for accelerating PDEs Simulations

Partial Differential Equations are foundational in modeling science and natural systems such as fluid dynamics and weather forecasting. The Latent Evolution of PDEs method is designed to address the computational intensity of classical and deep learning-based PDE solvers by proposing a scalable and efficient alternative. To enhance the efficiency and accuracy of LE-PDE, we incorporate the Mamba model, an advanced machine learning model known for its predictive efficiency and robustness in handling complex dynamic systems with a progressive learning strategy. The LE-PDE was tested on several benchmark problems. The method demonstrated a marked reduction in computational time compared to traditional solvers and standalone deep learning models while maintaining high accuracy in predicting system behavior over time. Our method doubles the inference speed compared to the LE-PDE while retaining the same level of parameter efficiency, making it well-suited for scenarios requiring long-term predictions.

DamFormer: Generalizing Morphologies in Dam Break Simulations Using Transformer Model

The interaction of waves with structural barriers such as dams breaking plays a critical role in flood defense and tsunami disasters. In this work, we explore the dynamic changes in wave surfaces impacting various structural shapes, e.g., circle, triangle, and square, by using deep learning techniques. We introduce the DamFormer, a novel transformer-based model designed to learn and simulate these complex interactions. The model was trained and tested on simulated data representing the three structural forms.