Related papers: Interpreting neural operators: how nonlinear waves…
We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on i) the localization volume of a mode which defines the number of interacting partner modes, ii) the overlap…
Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…
Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…
A robust energy transfer mechanism is found in nonlinear wave systems, which favours transfers towards modes interacting via non-resonant triads, applicable in meteorology, nonlinear optics and plasma wave turbulence. Transfer efficiency is…
Recently, neural operators have emerged as powerful tools for learning mappings between function spaces, enabling data-driven simulations of complex dynamics. Despite their successes, a deeper understanding of their learning mechanisms…
In this article we use analytical and numerical modeling to describe parallel viscous two-phase flows in microchannels. The focus is on idealized two-dimensional geometries, with a view to validating the various methodologies for future…
In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…
Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous…
The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the…
It has been suggested recently that growth and division of a protocell could be modeled by a chemically active droplet with simple chemical reactions driven by an external fuel supply. This model is called the continuum model. Indeed it's…
Neural operators have emerged as powerful tools for learning nonlinear mappings between function spaces, enabling real-time prediction of complex dynamics in diverse scientific and engineering applications. With their growing adoption in…
This paper advances the study of multivariate function approximation using neural network operators activated by symmetrized and perturbed hyperbolic tangent functions. We propose new non-linear operators that preserve dynamic symmetries…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…
We study the behaviour of catalytically active droplets in multi-component conserved mixtures affected by noise. Working in the thin interface limit, we analytically determine the state diagram of the system, characterized by multiple…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled…