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This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics.…

Analyzing data from dynamical systems often begins with creating a reconstruction of the trajectory based on one or more variables, but not all variables are suitable for reconstructing the trajectory. The concept of nonlinear observability…

We present a novel method for the classification and reconstruction of time dependent, high-dimensional data using sparse measurements, and apply it to the flow around a cylinder. Assuming the data lies near a low dimensional manifold…

Compressed sensing theory indicates that selecting a few measurements independently at random is a near optimal strategy to sense sparse or compressible signals. This is infeasible in practice for many acquisition devices that acquire sam-…

A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…

We propose a novel method to reconstruct volumetric flows from sparse views via a global transport formulation. Instead of obtaining the space-time function of the observations, we reconstruct its motion based on a single initial state. In…

Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent…

The problem of how many trajectories of a random walker in a potential are needed to reconstruct the values of this potential is studied. We show that this problem can be solved by calculating the probability of survival of an abstract…

Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…

We study phaseless sampling in spline spaces generated by B-splines with arbitrary knots. For real spline spaces, we give a necessary and sufficient condition for a sequence of sampling points to admit a local phase retrieval of any…

We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…

The observation of light super-partners from a supersymmetric extension to the Standard Model is an intensely sought-after experimental outcome, providing an explanation for the stabilization of the electroweak scale and indicating the…

We present a local Fourier slice equation that enables local and sparse projection of a signal. Our result exploits that a slice in frequency space is an iso-parameter set in spherical coordinates. Therefore, the projection of suitable…

A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based…

This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only…

We present a comparative experimental study of planar curves arising from a Fourier series whose frequencies are the prime numbers, together with several randomized control models. Starting from the series $F_n(t)=\sum_{p\le n} v_p(n!)\,…

Reconstructing a quantum system's Hamiltonian from limited yet experimentally observable information is interesting both as a practical task and from a fundamental standpoint. We pose and investigate the inverse problem of reconstructing a…

This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…

In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in…