Related papers: Hidden Fluid Mechanics: A Navier-Stokes Informed D…
We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…
Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…
Fluid-structure interaction is common in engineering and natural systems, where floating-body motion is governed by added mass, drag, and background flows. Modeling these dissipative dynamics is difficult: black-box neural models regress…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…
We present a novel method for guaranteeing linear momentum in learned physics simulations. Unlike existing methods, we enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional…
Hydrodynamics provides a universal description of the emergent collective dynamics of vastly different many-body systems, based solely on their symmetries and conservation laws. Here we harness this universality, encoded in the…
This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities…
We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an $H(\mathrm{div})$-conforming space,…
Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations by embedding governing physics into neural-network training. Recent studies have shown that parameterized PINNs can learn…
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…
An immersed-boundary method for the incompressible Navier--Stokes equations is presented. It employs discrete forcing for a sharp discrimination of the solid-fluid interface, and achieves second-order accuracy, demonstrated in examples with…
The present study investigates the accurate inference of Reynolds-averaged Navier-Stokes solutions for the compressible flow over aerofoils in two dimensions with a deep neural network. Our approach yields networks that learn to generate…
We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with…
Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems…
Subsurface geomodeling plays a critical role in reservoir characterization, uncertainty quantification, and subsurface flow prediction. However, integrating heterogeneous sources of geological information, including conceptual geological…
Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
The Holomorphic Embedding Load-Flow Method (HELM) was recently introduced as a novel technique to constructively solve the power-flow equations in power grids, based on advanced complex analysis. In this paper, the theoretical foundations…
We describe recent developments in the hybrid atomistic/continuum modelling of dense fluids. We discuss the general implementation of mass, momentum and energy transfers between a region described by molecular dynamics and the neighbouring…