相关论文: Project and Generate: Divergence-Free Neural Opera…

Wall-pressure fluctuations in turbulent boundary layers drive flow-induced noise, structural vibration, and hydroacoustic disturbances, especially in underwater and aerospace systems. Accurate prediction of their wavenumber-frequency…

The divergence theorem of Gauss plays a central role in the derivation of the governing differential equations in fluid dynamics, electrodynamics, gravitational fields, and optics. One is often interested in an evolution equation for the…

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…

We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…

In this article, we consider exactly divergence-free $H$(div)-conforming finite element methods for time-dependent incompressible viscous flow problems. This is an extension of previous research concerning divergence-free $H^1$-conforming…

Computational fluid dynamics (CFD) provides high-fidelity simulations of fluid flows but remains computationally expensive for many-query applications. In recent years deep learning (DL) has been used to construct data-driven fluid-dynamic…

The ability of Flow Matching (FM) to model complex conditional distributions has established it as the state-of-the-art for prediction tasks (e.g., robotics, weather forecasting). However, deployment in safety-critical settings is hindered…

We present an explicit divergence-free DG method for incompressible flow based on velocity formulation only. A globally divergence-free finite element space is used for the velocity field, and the pressure field is eliminated from the…

We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…

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

By framing reinforcement learning as a sequence modeling problem, recent work has enabled the use of generative models, such as diffusion models, for planning. While these models are effective in predicting long-horizon state trajectories…

Reconstructing dynamic 4D scenes is an important yet challenging task. While 3D foundation models like VGGT excel in static settings, they often struggle with dynamic sequences where motion causes significant geometric ambiguity. To address…

In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable density, compressible turbulent mixing. Though models of this kind (Reynolds Averaged Navier…

High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…

The class of Divergence-free symmetric tensors is ubiquitous in Continuum Mechanics. We show its invariance under projective transformations of the independent variables. This action, which preserves the positiveness, extends Sophus Lie's…

We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most…

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…