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.
Abstract (translated)
偏微分方程在建模科学和自然系统（如流体动力学和天气预报）中是基础性的。PDEs的隐式演化方法旨在通过提出一种可扩展且高效的替代方案来解决经典及基于深度学习的PDE求解器计算量大的问题。为了提高LE-PDE的效率和准确性，我们引入了Mamba模型，这是一种先进的机器学习模型，以其在处理复杂动态系统时的预测效率和鲁棒性而闻名，并采用了一种渐进的学习策略。LE-PDE在几个基准问题上进行了测试。该方法与传统的求解器及独立的深度学习模型相比，在保持高精度的同时显著减少了计算时间。我们的方法将推理速度提高了一倍，同时保留了相同的参数效率水平，使其非常适合需要长期预测的情景。
URL
https://arxiv.org/abs/2411.01897
