适用于高维混沌系统中非高斯数据同化的基于分数的粒子流滤波器
A score-based particle flow filter for non-Gaussian data assimilation in high-dimensional chaotic systems
AI总结：
针对现有粒子流滤波器无法捕捉混沌系统非高斯结构的问题，提出Score-PFF，通过神经网络学习的分数函数替代高斯先验，在高维混沌系统数据同化中实现误差降低与计算成本优化，性能优于相关基准方法。
AI中文摘要：
当前粒子流滤波器依赖高斯先验假设，无法捕捉混沌系统的非高斯吸引子结构。本研究提出一种基于分数的粒子流滤波器（Score-based Particle Flow Filter，Score-PFF），该方法通过去噪分数匹配用神经网络学习到的分数函数替代参数化先验梯度，从而能够灵活刻画混沌动力学中的多模态、偏斜及复杂先验分布。纯先验调整实验显示，Score-PFF的梯度方向正确指向吸引子，相比高斯先验可降低26.9%-29.0%的误差；在线性观测场景下，Score-PFF的性能显著优于高斯粒子流滤波器（Gaussian PFF）和集合调整卡尔曼滤波器（EAKF），其 Cohen's d 值分别为1.03和1.40，且能保留非高斯结构，而EAKF会逐步将其高斯化；在非线性观测算子下，Score-PFF在强非高斯 regime 中仍保持鲁棒性能，RMSE 降低可达60%；在1000维洛伦兹-96（Lorenz-96）系统上，Score-PFF相比PFF实现49.5%的RMSE降低，同时通过用神经网络推理替代基于奇异值分解（SVD）的协方差逆运算，降低了每次同化的计算成本。Score-PFF构建了一个计算上易处理的非高斯数据同化框架，适用于高维地球物理系统。
英文摘要：
Current particle flow filters rely on Gaussian prior assumptions that fail to capture the non-Gaussian attractor structure of chaotic systems. This study proposes a Score-based Particle Flow Filter (Score-PFF) that replaces the parametric prior gradient with a neural network-learned score function via denoising score matching. This enables flexible characterization of multimodal, skewed, and complex prior distributions in chaotic dynamics. Pure prior adjustment experiments demonstrate correct gradient directions toward the attractor (26.9%-29.0% error reduction over Gaussian priors). Under linear observations, Score-PFF significantly outperforms both Gaussian PFF and EAKF (Cohen's d = 1.03 and 1.40), preserving non-Gaussian structure that EAKF progressively Gaussianizes. Under nonlinear observation operators, Score-PFF maintains robust performance with up to 60% RMSE reduction in strongly non-Gaussian regimes. On the 1000-dimensional Lorenz-96 system, Score-PFF achieves 49.5% RMSE reduction over PFF while reducing per-assimilation cost by replacing SVD-based covariance inversion with neural network inference. Score-PFF establishes a computationally tractable, non-Gaussian data assimilation framework suitable for high-dimensional geophysical systems.
