Related papers: Lagrangian Flow Networks for Conservation Laws
Accurately predicting the future fluid is vital to extensive areas such as meteorology, oceanology, and aerodynamics. However, since the fluid is usually observed from the Eulerian perspective, its moving and intricate dynamics are…
The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation,…
We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time…
New aspects of turbulence are uncovered if one considers flow motion from the perspective of a fluid particle (known as the Lagrangian approach) rather than in terms of a velocity field (the Eulerian viewpoint). Using a new experimental…
Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy.…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…
Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-posedness and existence of a flow for RDEs with Osgood…
This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors. Our method first pretrains a flow model on the target features to capture the…
Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…
Reconstructions of Lagrangian drift, for example for objects lost at sea, are often uncertain due to unresolved physical phenomena within the data. Uncertainty is usually overcome by introducing stochasticity into the drift, but this…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…
Incorporating neural networks for the solution of Ordinary Differential Equations (ODEs) represents a pivotal research direction within computational mathematics. Within neural network architectures, the integration of the intrinsic…
The DFLU numerical flux was introduced in order to solve hyperbolic scalar conservation laws with a flux function discontinuous in space. We show how this flux can be used to solve certain class of systems of conservation laws such as…
Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through…
Elucidating reaction mechanisms hinges on efficiently generating transition states (TSs), products, and complete reaction networks. Recent generative models, such as diffusion models for TS sampling and sequence-based architectures for…
The advantage of particle Lagrangian methods in computational fluid dynamics is that advection is accurately modeled. However, this complicates the calculation of space derivatives. If a mesh is employed, it must be updated at each time…
In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation…
On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…
Diffusion-based models have significant achievements in time series generation but suffer from inefficient computation: solving high-dimensional ODEs/SDEs via iterative numerical solvers demands hundreds to thousands of drift function…