Related papers: Phase autoencoder for rapid data-driven synchroniz…
An asymptotic equation of motion for the pattern interface in the domain-forming reaction-diffusion systems is derived. The free boundary problem is reduced to the universal equation of non-local contour dynamics in two dimensions in the…
A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state…
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…
Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…
We develop a method for computing the stochastic wave speed of pulse solutions in kinematic equations subject to small stochastic forcing based on the isochronal phase reduction. These kinematic equations arise as the singular limit of…
The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic…
In this paper, we present a novel trajectory prediction model for autonomous driving, combining a Characterized Diffusion Module and a Spatial-Temporal Interaction Network to address the challenges posed by dynamic and heterogeneous traffic…
In present paper we discuss the control of complex spatio-temporal dynamics in a {spatially extended} non-linear system (fluid model of Pierce diode) based on the concepts of controlling chaos in the systems with few degrees of freedom. A…
Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…
Here we present a study of stochastic resonance in an extended FitzHugh-Nagumo system with a field dependent activator diffusion. We show that the system response (here measured through the output signal-to-noise ratio) is enhanced due to…
Being spontaneous, micro-expressions are useful in the inference of a person's true emotions even if an attempt is made to conceal them. Due to their short duration and low intensity, the recognition of micro-expressions is a difficult task…
With the growing size and complexity of turbulent flow models, data compression approaches are of the utmost importance to analyze, visualize, or restart the simulations. Recently, in-situ autoencoder-based compression approaches have been…
Diffusion models exhibit impressive scalability in robotic task learning, yet they struggle to adapt to novel, highly dynamic environments. This limitation primarily stems from their constrained replanning ability: they either operate at a…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In…
Current large-scale diffusion models represent a giant leap forward in conditional image synthesis, capable of interpreting diverse cues like text, human poses, and edges. However, their reliance on substantial computational resources and…
Understanding foggy image sequence in the driving scenes is critical for autonomous driving, but it remains a challenging task due to the difficulty in collecting and annotating real-world images of adverse weather. Recently, the…
We analyze several aspects of the phenomenon of stochastic resonance in reaction-diffusion systems, exploiting the nonequilibrium potential's framework. The generalization of this formalism (sketched in the appendix) to extended systems is…
In this paper we show that the analysis of the dynamics in localized regions, i.e., sub-systems can be used to characterize the chaotic dynamics and the synchronization ability of the spatiotemporal systems. Using noisy scalar time-series…
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…