Related papers: Dynamics and Synchrony from Oscillatory Data via D…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…

The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques combine physical models and observational data, often in a…

Building on the phase reduction theory formulated for reaction-diffusion systems with spatial translational symmetry, we develop a data-driven method that reconstructs the spatiotemporal phase dynamics of traveling and oscillating patterns.…

Human movement prediction is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose a prediction framework that decouples short-term…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

Finding interpretable biomechanical models can provide insight into the functionality of organs with regard to physiology and disease. However, identifying broadly applicable dynamical models for in vivo tissue remains challenging. In this…

Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from…

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…

In this paper we use the parameterization method to provide a complete description of the dynamics of an $n$-dimensional oscillator beyond the classical phase reduction. The parameterization method allows, via efficient algorithms, to…

A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…

Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with…

The dynamics of large systems of coupled oscillators is a subject of increasing importance with prominent applications in several areas such as physics and biology. The Kuramoto model, where a set of oscillators move around a circle…

Learning to model how the world changes as time elapses has proven a challenging problem for the computer vision community. We propose a self-supervised solution to this problem using temporal cycle consistency jointly in vision and…

Human trajectory anomaly detection has become increasingly important across a wide range of applications, including security surveillance and public health. However, existing trajectory anomaly detection methods are primarily focused on…

Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale…

Monitoring urban structure and development requires high-quality data at high spatiotemporal resolution. While traditional censuses have provided foundational insights into demographic and socioeconomic aspects of urban life, their pace may…

Predicting human motion in unstructured and dynamic environments is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose to encode…