The weak graph Koopman bilinear form model is proposed, which integrates geometric deep learning and Koopman theory to learn latent-space dynamics for networked systems, especially for challenging cases that have multiple timescales.
Visual localization is vital for autonomous systems but remains challenging under dynamic conditions. Transformers offer strong temporal modeling at quadratic cost, while CNNs are efficient yet limited in long-range dependencies. Existing methods also lack robustness to illumination, weather, and seasonal changes, constraining real-world applicability. To address this, this paper proposes AdapseqNet, a dual-branch architecture that integrates stabilized state-space modeling with differential temporal enhancement. First, a stabilized state-space formulation featuring Lyapunov-constrained parameterization and adaptive discretization is proposed, ensuring asymptotic stability and linear computational complexity for reliable processing of extended sequences. Second, a selective Mamba architecture is developed to combine temporal-state modeling with content-aware gating, enabling adaptive feature selection that emphasizes discriminative cues while suppressing redundancy. Third, a differential enhancement module is designed to extract motion-invariant representations through symmetric temporal differencing and LSTM-based refinement, enhancing resilience to appearance variations caused by lighting, weather, and seasonal changes. Beyond architectural design, multi-scale feature fusion and output distribution control are incorporated to optimize representation quality and ensure consistency for similarity-based retrieval. Extensive experiments on multiple benchmarks demonstrate that AdapseqNet achieves a better localization accuracy across diverse and challenging conditions. Note to Practitioners—Visual localization is crucial for autonomous robots but often fails under varying lighting, weather, or seasonal conditions. We propose a dual-path approach: one path captures long-term patterns using control-inspired stable modeling, while the other extracts motion cues that remain consistent despite appearance changes. This combination enables accurate place recognition even in extreme environments. Our system operates efficiently on standard hardware and was tested on an indoor robot, achieving centimeter-level accuracy. This approach can enhance existing navigation systems without requiring additional sensors. Future work will focus on real-time optimization for outdoor deployment.
This work uses SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time closed-loop controller for high-dimensional and parametric dynamics, relying solely on limited state sensor readings, alleviating the curse of dimensionality.
This work proposes the Koopman Graph Dynamics framework to learn the structural dynamics by integrating the global linear evolution of the Koopman operator with the local topological priors of Graph Neural Networks and develops a KGD based Model Predictive Control strategy for tethered space systems.
Comprehensive experiments on the NGSIM dataset validate the proposed model, demonstrating robust performance across structured highway driving scenarios and both the accuracy and computational efficiency of the proposed architecture.
An efficient Mamba-based feature extraction framework for jointly encoding vehicle trajectories and map information is proposed and achieves superior performance in terms of minADE, minFDE, and minMR, while maintaining high computational efficiency.