Related papers: Topological Dynamics via Learned Hybrid Systems
This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
We present a novel method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the…
This is a self-contained tour of the Conley index and connection matrices. The starting point is Conley's fundamental theorem of dynamical systems. There is a short stop at the necessary topological background, before we proceed to the…
Inferring the underlying graph topology that characterizes structured data is pivotal to many graph-based models when pre-defined graphs are not available. This paper focuses on learning graphs in the case of sequential data in dynamic…
Understanding the dynamical behavior of complex systems is of exceptional relevance in everyday life, from biology to economy. In order to describe the dynamical organization of complex systems, existing methods require the knowledge of the…
Enabling robots to perform complex dynamic tasks such as picking up an object in one sweeping motion or pushing off a wall to quickly turn a corner is a challenging problem. The dynamic interactions implicit in these tasks are critical…
We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents.…
Outlier, or anomaly, detection is essential for optimal performance of machine learning methods and statistical predictive models. It is not just a technical step in a data cleaning process but a key topic in many fields such as fraudulent…
Advanced integration of logistics systems has been promoted for the sake of competitiveness and sustainability. Such efforts will enable more globally optimal and flexible operations by efficiently utilizing transportation capacity. At the…
Accurate and real-time traffic state prediction is of great practical importance for urban traffic control and web mapping services. With the support of massive data, deep learning methods have shown their powerful capability in capturing…
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…
The ability to model and predict ego-vehicle's surrounding traffic is crucial for autonomous pilots and intelligent driver-assistance systems. Acceleration prediction is important as one of the major components of traffic prediction. This…
Trajectory optimization methods have achieved an exceptional level of performance on real-world robots in recent years. These methods heavily rely on accurate analytical models of the dynamics, yet some aspects of the physical world can…
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…
We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…
In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data and has become an advantageous tool for us to study complex…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…