LE-PDE++: Mamba for accelerating PDEs Simulations

TL;DR

LE-PDE++ combines the Mamba model with the Latent Evolution of PDEs approach to significantly accelerate PDE simulations, reducing computational time while maintaining high accuracy for complex dynamic systems.

Contribution

The paper introduces LE-PDE++ which integrates Mamba into LE-PDE, achieving faster PDE simulations with improved efficiency and robustness over previous methods.

Findings

Marked reduction in computational time compared to traditional solvers.

Maintains high accuracy in long-term predictions.

Doubles inference speed while retaining parameter efficiency.

Abstract

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.