Related papers: Machine learning of hidden variables in multiscale…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
Active turbulence is a paradigmatic and fascinating example of self-organized motion at large scales occurring in active matter. We employ massive hydrodynamic simulations of suspensions of resolved model microswimmers to tackle the…
Turbulent flow remains a challenging subject, despite extensive efforts to find analytical descriptions. Modeling small scales of motion is crucial for saving time and resources in numerical simulations, particularly in industrial…
Obtaining dynamics models is essential for robotics to achieve accurate model-based controllers and simulators for planning. The dynamics models are typically obtained using model specification of the manufacturer or simple numerical…
Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as density functional theory or phase-space…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
Deep learning is increasingly becoming a promising pathway to improving the accuracy of sub-grid scale (SGS) turbulence closure models for large eddy simulations (LES). We leverage the concept of differentiable turbulence, whereby an…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
In this article, I present recent methods for the numerical simulation of fluid dynamics and the associated computational algorithms. The goal of this article is to explain how to model an incompressible fluid, and how to write a computer…
An inviscid two-dimensional fluid model with nonlinear dispersion that arises simultaneously in coarse-grained descriptions of the dynamics of the Euler equation and in the description of non-Newtonian fluids of second grade is considered.…
This work deals with the modeling of plasmas, which are charged-particle fluids. Thanks to machine leaning, we construct a closure for the one-dimensional Euler-Poisson system valid for a wide range of collision regimes. This closure, based…
On the micro- and nanoscale, classical hydrodynamic boundary conditions such as the no-slip condition no longer apply. Instead, the flow profiles exhibit ``slip`` at the surface, which is characterized by a finite slip length (partial…
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…
Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…
Deep learning method has attracted tremendous attention to handle fluid dynamics in recent years. However, the deep learning method requires much data to guarantee the generalization ability and the data of fluid dynamics are deficient.…
Integration of machine learning (ML) models of unresolved dynamics into numerical simulations of fluid dynamics has been demonstrated to improve the accuracy of coarse resolution simulations. However, when trained in a purely offline mode,…