Related papers: Predicting sparse circle maps from their dynamics
This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…
In this paper we present a data driven approach for approximating dynamical systems. A dynamics is approximated using basis functions, which are derived from maximization of the information-theoretic entropy, and can be generated directly…
Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3…
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…
We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…
Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications,…
Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…
We study the problem of reconstructing a multivariate trigonometric polynomial having only few non-zero coefficients from few random samples. Inspired by recent work of Candes, Romberg and Tao we propose to recover the polynomial by Basis…
This note considers the multidimensional unstructured sparse recovery problems. Examples include Fourier inversion and sparse deconvolution. The eigenmatrix is a data-driven construction with desired approximate eigenvalues and eigenvectors…
In search and surveillance applications in robotics, it is intuitive to spatially distribute robot trajectories with respect to the probability of locating targets in the domain. Ergodic coverage is one such approach to trajectory planning…
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…
Mathematical modeling is a powerful tool for describing, predicting, and understanding complex phenomena exhibited by real-world systems. However, identifying the equations that govern a system's dynamics from experimental data remains a…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
Conventional notions of generalization often fail to describe the ability of learned models to capture meaningful information from dynamical data. A neural network that learns complex dynamics with a small test error may still fail to…
A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…
Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…
Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a…