Related papers: Data-driven ODE modeling of the high-frequency com…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
The Gaussian radial function-based Regression (RfR) method is a data-driven modeling approach that utilizes physically understandable variables from scalar time series, constructed using delay coordinates and Gaussian radial basis…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
In this paper, we present a generic approach of a dynamical data-driven model order reduction technique for three-dimensional fluid-structure interaction problems. A low-order continuous linear differential system is identified from…
Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…
We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…
Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…
We propose a framework for modeling and estimating the state of controlled dynamical systems, where an agent can affect the system through actions and receives partial observations. Based on this framework, we propose the Predictive State…
A new approach called Flow Curvature Method has been recently developed in a book entitled Differential Geometry Applied to Dynamical Systems. It consists in considering the trajectory curve, integral of any n-dimensional dynamical system…
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…
Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals…
We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its…
The ability to predict future outcomes conditioned on observed video frames is crucial for intelligent decision-making in autonomous systems. Recently, deep recurrent architectures have been applied to the task of video prediction. However,…
Data-driven reduced-order models of the dynamics of complex flows are important for tasks related to design, understanding, prediction, and control. Many flows obey symmetries, and the present work illustrates how these can be exploited to…
Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…
Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…