Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review
Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …
Benchmarking sparse system identification with low-dimensional chaos
Sparse system identification is the data-driven process of obtaining parsimonious differential
equations that describe the evolution of a dynamical system, balancing model complexity …
equations that describe the evolution of a dynamical system, balancing model complexity …
Deep learning delay coordinate dynamics for chaotic attractors from partial observable data
A common problem in time-series analysis is to predict dynamics with only scalar or partial
observations of the underlying dynamical system. For data on a smooth compact manifold …
observations of the underlying dynamical system. For data on a smooth compact manifold …
[HTML][HTML] Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint
Despite the success of various methods in addressing the issue of spatial reconstruction of
dynamical systems with sparse observations, spatio-temporal prediction for sparse fields …
dynamical systems with sparse observations, spatio-temporal prediction for sparse fields …
Online calibration of deep learning sub-models for hybrid numerical modeling systems
S Ouala, B Chapron, F Collard, L Gaultier… - Communications …, 2024 - nature.com
Defining end-to-end (or online) training schemes for the calibration of neural sub-models in
hybrid systems requires working with an optimization problem that involves the solver of the …
hybrid systems requires working with an optimization problem that involves the solver of the …
Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework
S Ouala, B Chapron, F Collard… - … Learning: Science and …, 2023 - iopscience.iop.org
Bernard O Koopman proposed an alternative view of dynamical systems based on linear
operator theory, in which the time evolution of a dynamical system is analogous to the linear …
operator theory, in which the time evolution of a dynamical system is analogous to the linear …
Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data
The rapid increase of population and settlement structures in the Global South during recent
decades has motivated the development of suitable models to describe their formation and …
decades has motivated the development of suitable models to describe their formation and …
Autoregressive With Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Series
A Okuno, Y Morishita, Y Mototake - IEEE Access, 2024 - ieeexplore.ieee.org
This study delves into the domain of dynamical systems, specifically the forecasting of
dynamical time series defined through an evolution function. Traditional approaches in this …
dynamical time series defined through an evolution function. Traditional approaches in this …
Local stability guarantees for data-driven quadratically nonlinear models
M Peng - 2023 - search.proquest.com
Abstract Navier Stokes equations (NSEs) are complicated partial differential equations
(PDEs) to describe the motion of fluids which are computationally expensive to simulate …
(PDEs) to describe the motion of fluids which are computationally expensive to simulate …
Prediction of turbulent energy based on low-rank resolvent modes and machine learning
A modelling framework based on the resolvent analysis and machine learning is proposed
to predict the turbulent energy in incompressible channel flows. In the framework, the …
to predict the turbulent energy in incompressible channel flows. In the framework, the …