NN-ResDMD: Learning Koopman Representations for Complex Dynamics with Spectral Residuals

Analyzing long-term behaviors in high-dimensional nonlinear dynamical systems remains a significant challenge. The Koopman operator framework has emerged as a powerful tool to address this issue by providing a globally linear perspective on nonlinear dynamics. However, existing methods for approximating the Koopman operator and its spectral components, particularly in large-scale systems, often lack robust theoretical guarantees. Residual Dynamic Mode Decomposition (ResDMD) introduces a spectral residual measure to assess the convergence of the estimated Koopman spectrum, which helps filter out spurious spectral components. Nevertheless, it depends on pre-computed spectra, thereby inheriting their inaccuracies. To overcome its limitations, we introduce the Neural Network-ResDMD (NN-ResDMD), a method that directly estimates Koopman spectral components by minimizing the spectral residual. By leveraging neural networks, NN-ResDMD automatically identifies the optimal basis functions of the Koopman invariant subspace, eliminating the need for manual selection and improving the reliability of the analysis. Experiments on physical and biological systems demonstrate that NN-ResDMD significantly improves both accuracy and scalability, making it an effective tool for analyzing complex dynamical systems.

Enabling Level-4 Autonomous Driving on a Single $1k Off-the-Shelf Card

Autonomous driving is of great interest in both research and industry. The high cost has been one of the major roadblocks that slow down the development and adoption of autonomous driving in practice. This paper, for the first-time, shows that it is possible to run level-4 (i.e., fully autonomous driving) software on a single off-the-shelf card (Jetson AGX Xavier) for less than $1k, an order of magnitude less than the state-of-the-art systems, while meeting all the requirements of latency. The success comes from the resolution of some important issues shared by existing practices through a series of measures and innovations. The study overturns the common perceptions of the computing resources required by level-4 autonomous driving, points out a promising path for the industry to lower the cost, and suggests a number of research opportunities for rethinking the architecture, software design, and optimizations of autonomous driving.

Decentralized Multi-Agent Reinforcement Learning for Task Offloading Under Uncertainty

Multi-Agent Reinforcement Learning (MARL) is a challenging subarea of Reinforcement Learning due to the non-stationarity of the environments and the large dimensionality of the combined action space. Deep MARL algorithms have been applied to solve different task offloading problems. However, in real-world applications, information required by the agents (i.e. rewards and states) are subject to noise and alterations. The stability and the robustness of deep MARL to practical challenges is still an open research problem. In this work, we apply state-of-the art MARL algorithms to solve task offloading with reward uncertainty. We show that perturbations in the reward signal can induce decrease in the performance compared to learning with perfect rewards. We expect this paper to stimulate more research in studying and addressing the practical challenges of deploying deep MARL solutions in wireless communications systems.