This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman filters (ROAD-EnKFs) learn a latent low-dimensional surrogate model for the dynamics and a decoder that maps from the latent space to the state space. The learned dynamics and decoder are then used within an ensemble Kalman filter to reconstruct and forecast the state. Numerical experiments show that if the state dynamics exhibit a hidden low-dimensional structure, ROAD-EnKFs achieve higher accuracy at lower computational cost compared to existing methods. If such structure is not expressed in the latent state dynamics, ROAD-EnKFs achieve similar accuracy at lower cost, making them a promising approach for surrogate state reconstruction and forecasting.

翻译：本文提出了一种计算框架，用于重构和预测按照未知或计算成本高昂的动力系统演化的部分可观测状态。我们的降阶可自动微分集合卡尔曼滤波器（ROAD-EnKFs）为动力学学习了一个潜在的低维替代模型，并学习了一个从潜在空间映射到状态空间的解码器。然后，学习到的动力学和解码器被应用于集合卡尔曼滤波器中，以重构和预测状态。数值实验表明，若状态动力学表现出隐藏的低维结构，ROAD-EnKFs能以更低计算成本实现比现有方法更高的精度；若潜在状态动力学中不体现此类结构，ROAD-EnKFs也能以更低成本达到相似精度，使其成为状态替代重构与预测的一种有前景的方法。