Related papers: Topological Linear System Identification via Moder…
We propose and present a concept of Topological Distance (TD), obtained from the integration of trace distance over the generalized Brillouin zone, in order to characterize the topological transitions of non-Hermitian systems. Specifically,…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
In this paper, the possibility of detecting topological variations by observing output trajectories from networked linear time-invariant systems is investigated, where the network topology can be general, but the nodes have identical…
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…
The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
We consider the problem of estimating the state and unknown input for a large class of nonlinear systems subject to unknown exogenous inputs. The exogenous inputs themselves are modeled as being generated by a nonlinear system subject to…
We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of…
We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and…
A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…
This paper presents a system identification framework -- inspired by multi-task learning -- to estimate the dynamics of a given number of linear time-invariant (LTI) systems jointly by leveraging structural similarities across the systems.…
Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…
We study the problem of stabilizing an unknown partially observable linear time-invariant (LTI) system. For fully observable systems, leveraging an unstable/stable subspace decomposition approach, state-of-art sample complexity is…
With more distributed energy resources (DERs) connected to distribution grids, better monitoring and control are needed, where identifying the topology accurately is the prerequisite. However, due to frequent re-configurations, operators…
We use low-depth quantum circuits, a specific type of tensor networks, to classify two-dimensional symmetry-protected topological many-body localized phases. For (anti-)unitary on-site symmetries we show that the (generalized) third…
Identifying latent state representations and dynamics is essential when direct modeling in observation space is infeasible, particularly under partial and high-dimensional observations. In such settings, representation learning and…