AI 中文总结
针对高维非线性系统状态估计，提出端到端学习框架，用自动编码器神经网络和降阶线性时不变模型联合训练，学习面向任务的降阶模型，基于可微卡尔曼滤波器最小化多目标损失，并用共形预测量化性能差距，在热扩散基准测试中验证。
AI 中文摘要
我们提出了一个面向滤波的端到端学习框架，以识别专门为高维非线性系统状态估计量身定制的降阶模型。一个自动编码器（AE）神经网络学习状态的低维潜表示以及到原始空间的提升映射，而降阶线性时不变（RO-LTI）模型描述潜动态。AE和RO-LTI模型通过最小化一个多目标损失联合训练，该损失将基于可微卡尔曼滤波器的重建误差与滤波目标相结合，确保降阶模型适合下游状态估计任务。在推理时，使用RO-LTI模型在潜空间中完全执行滤波，并通过解码器将估计状态映射回原始空间。与传统的两阶段方法不同，所提出的框架学习一个面向任务的降阶模型，其参数完全由滤波性能而非仅系统逼近精度塑造。我们还使用共形预测量化了全阶和降阶滤波器性能差距的概率界，该方法无需对数据分布做假设。该方法在热扩散基准测试中得到验证，从稀疏测量中重建了完整温度场。
英文摘要
We propose a filtering-oriented end-to-end learning framework to identify reduced-order models explicitly tailored for state estimation in high-dimensional nonlinear systems. An autoencoder (AE) neural network learns a low-dimensional latent representation of the state together with a lifting map to the original space, while a reduced-order linear time-invariant (RO-LTI) model describes the latent dynamics. The AE and RO-LTI model are trained jointly by minimizing a multi-objective loss that combines reconstruction error with a filtering objective based on a differentiable Kalman filter, ensuring that the reduced-order model is tailored for the downstream state estimation task. At inference, filtering is performed entirely in the latent space using the RO-LTI model, and the estimated state is mapped back to the original space via the decoder. Unlike conventional two-stage approaches, in which a reduced-order model is first identified for system approximation and a filter is subsequently designed on top of it, the proposed framework learns a task-oriented reduced-order model whose parameters are shaped entirely by filtering performance rather than system approximation accuracy alone. We further quantify probabilistic bounds on the performance gap between full-order and reduced-order filters using conformal predictions, which do not require assumption on data distribution. The approach is validated on a heat diffusion benchmark, where the full temperature field is reconstructed from sparse measurements.
Comments8 pages, 4 figures, preprint accepted for publication in the proceedings of the 2026 65th IEEE Conference on Decision and Control (CDC), Hawaii, USA
