Related papers: Bridging data science and dynamical systems theory

Networks have been studied mainly using statistical methods. Here I collect some dynamical systems tools which are useful to study both the dynamics on networks and their evolution. They include decomposition of differential dynamics,…

Traditional statistical estimation, or statistical inference in general, is static, in the sense that the estimate of the quantity of interest does not change the future evolution of the quantity. In some sequential estimation problems…

In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…

In this article, we propose a data-enabled economic predictive control method for a class of nonlinear systems, which aims to optimize the economic operational performance while handling hard constraints on the system outputs. Two lifting…

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…

Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…

Although deep learning-based methods have shown great success in spatiotemporal predictive learning, the framework of those models is designed mainly by intuition. How to make spatiotemporal forecasting with theoretical guarantees is still…

We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

Supervised learning, characterized by both discriminative and generative learning, seeks to predict the values of single (or sometimes multiple) predefined target attributes based on a predefined set of predictor attributes. For…

Semi-supervised and unsupervised systems provide operators with invaluable support and can tremendously reduce the operators load. In the light of the necessity to process large volumes of video data and provide autonomous decisions, this…

Control of underactuated dynamical systems has been studied for decades in robotics, and is now emerging in other fields such as neuroscience. Most of the advances have been in model based control theory, which has limitations when the…

This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to regulate a dynamical system to the solution of an optimization…

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

The abundance of process operating data in modern industries, along with the rapid advancement of learning techniques, has led to a paradigm shift towards data-centric analysis and control. However, integrating machine learning with control…

Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…