用深度学习估算大气动力学的科普曼算子，提升模型可解释性。
Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics
- 构建卷积神经网络估计科普曼算子，实现非线性系统线性化
- 在理想化大气模型中实现与物理模型相当的预测精度
- 为数据驱动气象模型提供透明化分析工具，适合气候研究者
深度学习正在重塑天气预报，新提出的数据驱动模型在中期预测上的准确率已达到与业务物理模型相当的水平。然而，这些模型通常缺乏可解释性，其内在动力学机制难以理解。本文提出方法以估计科普曼算子，通过线性表示复杂非线性动力学，提升数据驱动模型的透明度。尽管前景广阔，将科普曼算子应用于大规模问题（如大气建模）仍面临挑战。本研究旨在识别现有方法的局限，优化模型以克服多重瓶颈，并引入新型卷积神经网络架构，捕捉简化的动力学特征。实验基于理想化大气动力学系统，验证了方法的有效性。
原文摘要 · Abstract (English)
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their underlying dynamics difficult to understand and explain. This paper proposes methodologies to estimate the Koopman operator, providing a linear representation of complex nonlinear dynamics to enhance the transparency of data-driven models. Despite its potential, applying the Koopman operator to large-scale problems, such as atmospheric modeling, remains challenging. This study aims to identify the limitations of existing methods, refine these models to overcome various bottlenecks, and introduce novel convolutional neural network architectures that capture simplified dynamics.
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