Related papers: A unifying approach to self-organizing systems int…
Constrained dynamical systems are systems such that, by some means, the state stays within a given set. Two such systems are the (perturbed) Moreau sweeping process and the recently proposed extended Projected Dynamical System (ePDS). We…
The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics, and has been widely undertaken. Typically, however, networks employed in theoretical…
Dynamic relational data arise in many machine learning applications, yet their evolving structure poses challenges for learning representations that remain consistent and interpretable over time. A common approach is to learn time varying…
Most object manipulation strategies for robots are based on the assumption that the object is rigid (i.e., with fixed geometry) and the goal's details have been fully specified (e.g., the exact target pose). However, there are many tasks…
The primary objective of this thesis is to develop novel algorithmic approaches for Graph Representation Learning of static and single-event dynamic networks. In such a direction, we focus on the family of Latent Space Models, and more…
Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling.…
We introduce a simple model of self-propelled agents connected by linear springs, with no explicit alignment rules. Below a critical noise level, the agents self-organize into a collectively translating or rotating group. We derive…
Biological transport networks are highly optimized structures that ensure power-efficient distribution of fluids across various domains, including animal vasculature and plant venation. Theoretically, these networks can be described as…
Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many…
We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek-Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological…
Diffusion policies generate robot motions by learning to denoise action-space trajectories conditioned on observations. These observations are commonly streams of RGB images, whose high dimensionality includes substantial task-irrelevant…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
Network embedding aims to embed nodes into a low-dimensional space, while capturing the network structures and properties. Although quite a few promising network embedding methods have been proposed, most of them focus on static networks.…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
A recurrent task in coordinated systems is managing (estimating, predicting, or controlling) signals that vary in space, such as distributed sensed data or computation outcomes. Especially in large-scale settings, the problem can be…
Newly arriving nodes in dynamics networks would gradually make the node embedding space drifted and the retraining of node embedding and downstream models indispensable. An exact threshold size of these new nodes, below which the node…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
The real world is awash with multi-agent problems that require collective action by self-interested agents, from the routing of packets across a computer network to the management of irrigation systems. Such systems have local incentives…
A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…
We study the behavior of classical dimer coverings of the square lattice - a paradigmatic model for systems subject to constraints - evolving under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We…