用生成式滤波器提升机器学习模型的长期预测稳定性。
A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systems
- 引入基于扩散模型的评分滤波器，无需训练即可融合观测数据
- 在洛伦兹-96和KdV方程中，预测不确定性显著降低
- 适合需要长期稳定预测的复杂系统建模任务
我们提出一种评分滤波增强型数据同化框架，旨在降低数据驱动动力系统预测中机器学习模型的不确定性。机器学习虽可高效模拟动力系统，但即使数据充足，模型误差仍会随时间累积，导致长期预测性能下降。为此，我们将数据同化技术融入训练过程，通过观测信息迭代修正预测。具体采用基于生成式AI的无训练扩散模型方法——集合评分滤波器（EnSF），解决高维非线性复杂系统的同化问题。该框架将机器学习与EnSF结合，形成混合同化-训练机制，有效提升长期预测能力。实验表明，经EnSF增强的机器学习模型在洛伦兹-96系统和Korteweg-De Vries（KdV）方程的预测中，均能显著减少预测不确定性。
原文摘要 · Abstract (English)
We introduce a score-filter-enhanced data assimilation framework designed to reduce predictive uncertainty in machine learning (ML) models for data-driven dynamical system forecasting. Machine learning serves as an efficient numerical model for predicting dynamical systems. However, even with sufficient data, model uncertainty remains and accumulates over time, causing the long-term performance of ML models to deteriorate. To overcome this difficulty, we integrate data assimilation techniques into the training process to iteratively refine the model predictions by incorporating observational information. Specifically, we apply the Ensemble Score Filter (EnSF), a generative AI-based training-free diffusion model approach, for solving the data assimilation problem in high-dimensional nonlinear complex systems. This leads to a hybrid data assimilation-training framework that combines ML with EnSF to improve long-term predictive performance. We shall demonstrate that EnSF-enhanced ML can effectively reduce predictive uncertainty in ML-based Lorenz-96 system prediction and the Korteweg-De Vries (KdV) equation prediction.
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