Related papers: Data-driven modeling of a settling sphere in a qui…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
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…
The simulation of turbulent flow requires many degrees of freedom to resolve all the relevant times and length scales. However, due to the dissipative nature of the Navier-Stokes equations, the long-term dynamics are expected to lie on a…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerically these equations can be extremely demanding. Several…
We formulate a data-driven method for constructing finite volume discretizations of a dynamical system's underlying Continuity / Fokker-Planck equation. A method is employed that allows for flexibility in partitioning state space,…
We study the evolution of nonlinear surface gravity water-wave packets developing from modulational instability over an uneven bottom. A nonlinear Schr\"odinger equation (NLSE) with coefficients varying in space along propagation is used as…
Under the right circumstances, inertial particles (such as sand or dust) settling through the atmospheric boundary layer can experience a net enhancement in their average settling velocity due to their inertia. Since this enhancement arises…
This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using…
We study the settling of suspensions of relatively large particles with a diameter of the order of ten Kolmogorov scales and density slightly larger than the carrier fluid in statistically steady homogeneous isotropic turbulence. The…
Smoothed Particle Hydrodynamics (SPH) is a popular numerical technique developed for simulating complex fluid flows. Among its key ingredients is the use of nonlocal integral relaxations to local differentiations. Mathematical analysis of…
We investigate the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More precisely we consider the limit where the thickness of these…
Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…
We investigate the collective dynamics of self-propelled droplets, confined in a one dimensional micro-fluidic channel. On one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other…
In this work we develop a theoretical framework for the localization of flow in the steadily flowing regime of sheared disordered solids with inertial dynamics on a microscopic scale. To this aim we perform rheology studies at fixed shear…