Related papers: Topological Linear System Identification via Moder…
For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…
In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
The topological classification of the inner mappings on the fully invariant regular components of the wandering set with a special attracting boundary up to the topological conjugacy is defined in terms of distinguishing graph. Two inner…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
Changes in the parameters of dynamical systems can cause the state of the system to shift between different qualitative regimes. These shifts, known as bifurcations, are critical to study as they can indicate when the system is about to…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
We solve the problem of identifying (reconstructing) network topology from steady state network measurements. Concretely, given only a data matrix $\mathbf{X}$ where the $X_{ij}$ entry corresponds to flow in edge $i$ in configuration…
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 study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…
In this paper we study the problem of inferring the initial conditions of a dynamical system under incomplete information. Studying several model systems, we infer the latent microstates that best reproduce an observed time series when the…
Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small…
Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…