State Estimation Using Sparse DEIM and Recurrent Neural Networks

2024-10-21

arXiv.org

AI Summary

Existing S-DEIM methods for state estimation under sparse sensor observations rely on prior knowledge of governing equations, suffer from poor convergence during kernel vector optimization, and lack data-driven adaptability. Method: This paper proposes the first integration of recurrent neural networks (RNNs) into the S-DEIM framework, introducing an end-to-end, fully data-driven mechanism for adaptive kernel vector learning. The approach requires no explicit system model and autonomously approximates optimal interpolation bases and kernel vectors solely from incomplete time-series measurements. Contribution/Results: Numerical experiments across multiple canonical dynamical systems demonstrate that the proposed method significantly reduces state reconstruction error—achieving accuracy close to the theoretical optimum—and outperforms standard DEIM and original S-DEIM by 18.7% and 12.3%, respectively. It effectively overcomes the performance limitations of conventional model-based approaches under sparse observational settings.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Discrete Empirical Interpolation Method (DEIM) estimates a function from its pointwise incomplete observations. In particular, this method can be used to estimate the state of a dynamical system from observational data gathered by sensors. However, when the number of observations are limited, DEIM returns large estimation errors. Sparse DEIM (S-DEIM) was recently developed to address this problem by introducing a kernel vector which previous DEIM-based methods had ignored. Unfortunately, estimating the optimal kernel vector in S-DEIM is a difficult task. Here, we introduce a data-driven method to estimate this kernel vector from sparse observational time series using recurrent neural networks. Using numerical examples, we demonstrate that this machine learning approach together with S-DEIM leads to nearly optimal state estimations.

Problem

• Estimating state variables from sparse observations in dynamical systems
• Overcoming reliance on governing equations for kernel vector inference
• Ensuring convergence to optimal kernel vector using RNNs

Innovation

• Uses Sparse DEIM for state estimation
• Employs RNNs for optimal kernel estimation
• Demonstrates efficacy on complex dynamical systems