用条件归一化流联合估计状态与参数，提升非线性系统的预测精度。
Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation
- 基于条件归一化流，通过MLP、Transformer或Mamba-SSM生成条件嵌入。
- 引入最优传输启发的动能损失，缓解大规模变换下的过参数化问题。
- 适用于自动驾驶、疫情预测等场景，支持时间反演与链式预测，适合复杂系统建模者。
传统滤波算法（如卡尔曼滤波、无迹卡尔曼滤波、粒子滤波）在处理不确定性为任意非高斯、多模态分布的非线性系统时性能下降。本文综述基于条件归一化流的非线性滤波方法，其中条件嵌入由标准MLP、Transformer或选择性状态空间模型（如Mamba-SSM）生成。此外，测试了受最优传输启发的动能损失项在缓解包含大量变换的流模型过参数化问题中的有效性。研究在自动驾驶与患者群体动态建模等应用中评估这些方法的表现，特别关注时间反演与链式预测能力。最后，评估多种条件策略在真实世界新冠联合SIR系统预测与参数估计任务中的表现。
原文摘要 · Abstract (English)
Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters -- show performance degradation when applied to nonlinear systems whose uncertainty follows arbitrary non-Gaussian, and potentially multi-modal distributions. This study reviews recent approaches to state estimation via nonlinear filtering based on conditional normalizing flows, where the conditional embedding is generated by standard MLP architectures, transformers or selective state-space models (like Mamba-SSM). In addition, we test the effectiveness of an optimal-transport-inspired kinetic loss term in mitigating overparameterization in flows consisting of a large collection of transformations. We investigate the performance of these approaches on applications relevant to autonomous driving and patient population dynamics, paying special attention to how they handle time inversion and chained predictions. Finally, we assess the performance of various conditioning strategies for an application to real-world COVID-19 joint SIR system forecasting and parameter estimation.
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