Related papers: Learning Dynamical Systems and Bifurcation via Gro…

Bifurcation diagram is a powerful tool that visually gives information about the behavior of the equilibrium points of a dynamical system respect to the varying parameter. This paper proposes an educational algorithm by which the local…

By extending the extreme learning machine by additional control inputs, we achieved almost complete reproduction of bifurcation structures of dynamical systems. The learning ability of the proposed neural network system is striking in that…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…

The behavior of many dynamical systems follow complex, yet still unknown partial differential equations (PDEs). While several machine learning methods have been proposed to learn PDEs directly from data, previous methods are limited to…

When modeling dynamical systems from real-world data samples, the distribution of data often changes according to the environment in which they are captured, and the dynamics of the system itself vary from one environment to another.…

A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by…

It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

We demonstrate the synthesis of sparse sampling and machine learning to characterize and model complex, nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper…

Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…

Learning dynamical systems is a promising avenue for scientific discoveries. However, capturing the governing dynamics in multiple environments still remains a challenge: model-based approaches rely on the fidelity of assumptions made for a…

Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful…

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…

Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

When training the parameters of a linear dynamical model, the gradient descent algorithm is likely to fail to converge if the squared-error loss is used as the training loss function. Restricting the parameter space to a smaller subset and…

Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically…

Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…

For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…

An adaptive sampling approach for efficient detection of bifurcation boundaries in parametrized fluid flow problems is presented herein. The study extends the machine-learning approach of Silvester~(J. Comput. Phys., 553 (2026), 114743),…