Related papers: Deep Learning of Conjugate Mappings
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…
We introduce a data-driven method and shows its skills for spatiotemporal prediction of high-dimensional chaotic dynamics and turbulence. The method is based on a finite-dimensional approximation of the Koopman operator where the…
This paper extends our previous work~(Szumi\'nski and Maciejewski, 2024), where we explored the dynamics and integrability of the double-spring pendulum. Here, we investigate the variable-length double pendulum, a three-degree-of-freedom…
The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has lead to the generation of some coupled chaotic maps with an invariant measure. It is shown that these…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
The phenomenon of intrinsic localization in discrete nonlinear extended systems, i.e. the (generic) existence of discrete breathers, is shown to be not restricted to periodic solutions but it also extends to more complex (chaotic) dynamical…
The dominant way to control a robot manipulator uses hand-crafted differential equations leveraging some form of inverse kinematics / dynamics. We propose a simple, versatile joint-level controller that dispenses with differential equations…
We investigate whether a strongly turbulent flow with intermittent large-scale reorganizations admits a compact state-space description. As a representative high-dimensional chaotic system we consider two-dimensional Rayleigh--B\'enard…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
The integrability of two symplectic maps, that can be considered as discrete-time analogs of the Garnier and Neumann systems is established in the framework of the $r$-matrix approach, starting from their Lax representation. In contrast…
The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…
This paper studies the dynamics and integrability of a variable-length coupled pendulum system. The complexity of the model is presented by joining various numerical methods, such as the Poincar\'e cross-sections, phase-parametric diagrams,…
Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large…