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Rapid developments in advanced sensing and imaging have significantly enhanced information visibility, opening opportunities for predictive modeling of complex dynamic systems. However, sensing signals acquired from such complex systems are…
A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. It was proved in [Avigad et al. 2010,…
Graph is a ubiquitous structure in many domains. The rapidly increasing data volume calls for efficient and scalable graph data processing. In recent years, designing distributed graph processing systems has been an increasingly important…
Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic…
For every positive integer $n\geq 2$, we introduce the concept of measure-theoretic $n$-sensitivity for measure-theoretic dynamical systems via finite measurable partitions, and show that an ergodic system is measure-theoretically…
For smooth random dynamical systems we consider the quenched linear and higher-order response of equivariant physical measures to perturbations of the random dynamics. We show that the spectral perturbation theory of Gou\"ezel, Keller, and…
This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random input. The first method represents a novel integration of…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
In this study, we introduce a sensitivity analysis methodology for stochastic systems in chemistry, where dynamics are often governed by random processes. Our approach is based on gradient estimation via finite differences, averaging…
This paper develops KL-Ergodic Exploration from Equilibrium ($\text{KL-E}^3$), a method for robotic systems to integrate stability into actively generating informative measurements through ergodic exploration. Ergodic exploration enables…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order…
The study of experimental data is a relevant task in several physical, chemical and biological applications. In particular, the analysis of chaotic dynamics in cardiac systems is crucial as it can be related to some pathological…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
The understanding of adaptive algorithms for SDEs is an open area where many issues related to both convergence and stability (long time behaviour) of algorithms are unresolved. This paper considers a very simple adaptive algorithm, based…
This letter presents a non-parametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion…
The real-time prediction of chaotic systems requires a nonlinear-reduced order model (ROM) to forecast the dynamics, and a stream of data from sensors to update the ROM. Data-driven ROMs are typically built with a two-step strategy: data…
Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the…