Related papers: Predicting Flow Dynamics using Diffusion Models
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows…
The majority of practical flows, particularly those flows in applications of importance to transport, distribution and climate, are turbulent and as a result experience complex three-dimensional motion with increased drag compared with the…
We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of…
Diffusion and flow matching models have achieved remarkable success in text-to-image generation. However, these models typically rely on the predetermined denoising schedules for all prompts. The multi-step reverse diffusion process can be…
Real-time and accurate prediction of aerodynamic flow fields around airfoils is crucial for flow control and aerodynamic optimization. However, achieving this remains challenging due to the high computational costs and the non-linear nature…
We develop a diffuse solid method that is versatile and accurate for modeling wetting and multiphase flows in highly complex geometries. In this scheme, we harness N + 1-component phase field models to investigate interface shapes and flow…
Numerical simulation results of basic exactly solvable fluid flows using the previously proposed Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H.…
Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
Diffusion models, which leverage stochastic processes to capture complex data distributions effectively, have shown their performance as generative models, achieving notable success in image-related tasks through iterative denoising…
Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…
Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…
We present a method to downscale idealized geophysical fluid simulations using generative models based on diffusion maps. By analyzing the Fourier spectra of images drawn from different data distributions, we show how one can chain together…
Accurate traffic flow prediction is essential for applications like transport logistics but remains challenging due to complex spatio-temporal correlations and non-linear traffic patterns. Existing methods often model spatial and temporal…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…