Closure problems are omnipresent when simulating multiscale systems, where some
quantities and processes cannot be fully prescribed despite their effects on the simulation's …

Forecasting high-dimensional dynamical systems is a fundamental challenge in various
fields, such as geosciences and engineering. Neural Ordinary Differential Equations …

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in
computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive …

We propose a new neural network based large eddy simulation framework for the
incompressible Navier-Stokes equations based on the paradigm “discretize first, filter and …

In turbulence modeling, we are concerned with finding closure models that represent the
effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards …

Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear
partial differential equations, is crucial in various scientific and engineering applications …

Solving fluid dynamics equations often requires the use of closure relations that account for
missing microphysics. For example, when solving equations related to fluid dynamics for …

This work integrates machine learning into an atmospheric parameterization to target
uncertain mixing processes while maintaining interpretable, predictive, and well‐established …

We propose a new approach to learning the subgrid-scale model when simulating partial
differential equations (PDEs) solved by the method of lines and their representation in …

Accurately predicting the long-term behavior of chaotic systems is crucial for various
applications such as climate modeling. However, achieving such predictions typically …