- 控制理论和非线性滤波讨论班

Universal Approximation Capacity of Bidirectional Recurrent Neural Networks with Noisy Sequential Inputs

组织者

丘成栋

演讲者

陶飏天择

时间

2023年08月28日 15:00 至 15:30

地点

数学系理科楼A-203

摘要

In this presentation, we undertake an investigation into the capacity of bidirectional recurrent neural networks (BRNNs) to approximate filtering and smoothing dynamics under the state-space models (SSMs) framework in the presence of noisy sequential inputs. Our analysis initially establishes, under certain reasonable assumptions, that the forward recursions of BRNNs are capable of accurately approximating any filtering dynamics, while the backward recursions of BRNNs satisfactorily approximate the corresponding smoothing dynamics. We present explicit estimation bounds for both filtering and smoothing dynamics and utilize these theoretical results to construct a BRNN-Based smoother, which offers a synthetic resolution to the optimal smoothing problem. By training a BRNN on sequences of observations and their corresponding states produced by computer simulations or actual experiments, we demonstrate that the BRNN-Based smoother can closely approximate the optimal smoother, including approximating the optimal filter as its forward recursion. Finally, we support our theoretical findings through two examples and compare our results numerically against the extended Kalman smoother (EKS) and particle smoother (PS).