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The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators…

With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the…

Coupled nonlinear oscillators, e.g., Kuramoto models, are commonly used to analyze electrical power systems. The cage model from statistical mechanics has also been used to describe the dynamics of synchronously connected generation…

We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics…

The Kuramoto model with high-order coupling has recently attracted some attention in the field of coupled oscillators in order, for instance, to describe clustering phenomena in sets of coupled agents. Instead of considering interactions…

Developing physics-based models for molecular simulation requires fitting many unknown parameters to diverse experimental datasets. Traditionally, this process is piecemeal and difficult to reproduce, leading to a fragmented landscape of…

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…

We present a method that exploits self-consistent simulation of coarse-grained and fine-grained models, in order to analyse properties of physical systems. The method uses the coarse-grained model to obtain a first estimate of the quantity…

We study a generalized Kuramoto model in which each oscillator carries two coupled phase variables, representing a minimal swarmalator system. Assuming perfect correlation between the intrinsic frequencies associated with each phase…

Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role…

A model reduction technique based on an optimization principle is employed to coarse-grain inviscid, incompressible fluid dynamics in two dimensions. In this reduction the spectrally-truncated vorticity equation defines the microdynamics,…

Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more…

The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…

The issue of the parameterization of small-scale dynamics is addressed in the context of passive-scalar turbulence. The basic idea of our strategy is to identify dynamical equations for the coarse-grained scalar dynamics starting from…

A coarse-grained simulation model eliminates microscopic degrees of freedom and represents a polymer by a simplified structure. A priori, two classes of coarse-grained models may be distinguished: those which are designed for a specific…

Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled…

The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…

The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make…