用Mamba加速偏微分方程模拟，推理速度翻倍且保持精度。
LE-PDE++: Mamba for accelerating PDEs Simulations
- 引入Mamba模型提升LE-PDE的动态系统建模效率。
- 推理速度比原方法快一倍，长期预测误差小。
- 适合需要快速、高精度长期仿真的科学计算场景。
偏微分方程是流体动力学、天气预报等科学与自然系统建模的基础。为解决传统求解器和基于深度学习的求解器计算成本高的问题，本文提出一种可扩展、高效的潜变量演化方法（LE-PDE）。为进一步提升效率与精度，引入Mamba模型——一种具备高效预测能力且对复杂动态系统鲁棒的先进机器学习模型，并采用渐进式学习策略。在多个基准问题上测试表明，该方法相比传统求解器和独立深度学习模型显著降低计算时间，同时保持对系统行为随时间演化的高精度预测。相较于原始LE-PDE，本方法推理速度提升一倍，参数效率不变，适用于需要长期预测的场景。
原文摘要 · Abstract (English)
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.
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