Real-time state estimation is essential for conducting fast structural health assessment and enabling high-rate systems feedback control. High-rate systems are dynamic systems that experience extreme acceleration (> 100 g) within very short periods (< 1 ms), such as hypersonic systems and impact mitigation mechanisms. These engineering systems require control and feedback strategies capable of operating within sub-millisecond ranges, posing significant challenges for traditional prediction methods that analyze nonlinear and nonstationary behavior. This paper presents a machine learning framework that combines topological data analysis (TDA) with recurrent neural networks (RNNs) to improve prediction speed and accuracy in high-rate environments. The proposed architecture is an ensemble of parallel RNNs with long short-term memory (LSTM) cells, each trained on a distinct but selected delay vector based on the physical characteristics of the system. A novel advancement is the replacement of traditional back-propagation (BP)-based attention mechanisms with a feedforward strategy based on a TDA metric feature, specifically the maximum persistence of the first dimension of ingested data’s persistence homology group (max(<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_1\)</EquationSource> </InlineEquation>)), thus creating an architecture termed topology-informed deep learning estimator (TIDLE). In TIDLE, the max(<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H_1\)</EquationSource> </InlineEquation>) estimates the current system’s state and computes dynamic weights towards combining the RNN outputs, and mitigates the need for gradient-based updates during prediction, significantly reducing computation time and providing reliable dynamic context to the deep learner. Training is performed using synthetic cosine signals, eliminating the need for labeled experimental data and enhancing generalization in data-scarce conditions. TIDLE is validated on both synthetic and experimental datasets from the Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research (DROPBEAR) testbed. Results show improved accuracy over BP attention-based ensembles, especially at longer prediction horizons and during stationary periods. TIDLE achieves real-time prediction with an average computation time of 5.1 ms per step, a 27% speed improvement over state-of-the art attention-based modeling. These results highlight the potential of topology-informed deep and machine learning architectures for making fast and accurate predictions in high-rate system applications.

Topology-informed deep learning estimation using feedforward attention layer for high-rate state estimation

期刊论文
发表日期：

2026年6月23日

查看全文

Arman Razmarashooli,
Metrid Okumu,
Daniel Salazar,
Yang Kang Chua,
Simon Laflamme,
Chao Hu,
Paul T. Schrader,
Erik Blasch

摘要

Real-time state estimation is essential for conducting fast structural health assessment and enabling high-rate systems feedback control. High-rate systems are dynamic systems that experience extreme acceleration (> 100 g) within very short periods (< 1 ms), such as hypersonic systems and impact mitigation mechanisms. These engineering systems require control and feedback strategies capable of operating within sub-millisecond ranges, posing significant challenges for traditional prediction methods that analyze nonlinear and nonstationary behavior. This paper presents a machine learning framework that combines topological data analysis (TDA) with recurrent neural networks (RNNs) to improve prediction speed and accuracy in high-rate environments. The proposed architecture is an ensemble of parallel RNNs with long short-term memory (LSTM) cells, each trained on a distinct but selected delay vector based on the physical characteristics of the system. A novel advancement is the replacement of traditional back-propagation (BP)-based attention mechanisms with a feedforward strategy based on a TDA metric feature, specifically the maximum persistence of the first dimension of ingested data’s persistence homology group (max( \(H_1\) )), thus creating an architecture termed topology-informed deep learning estimator (TIDLE). In TIDLE, the max( \(H_1\) ) estimates the current system’s state and computes dynamic weights towards combining the RNN outputs, and mitigates the need for gradient-based updates during prediction, significantly reducing computation time and providing reliable dynamic context to the deep learner. Training is performed using synthetic cosine signals, eliminating the need for labeled experimental data and enhancing generalization in data-scarce conditions. TIDLE is validated on both synthetic and experimental datasets from the Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research (DROPBEAR) testbed. Results show improved accuracy over BP attention-based ensembles, especially at longer prediction horizons and during stationary periods. TIDLE achieves real-time prediction with an average computation time of 5.1 ms per step, a 27% speed improvement over state-of-the art attention-based modeling. These results highlight the potential of topology-informed deep and machine learning architectures for making fast and accurate predictions in high-rate system applications.