Related papers: Reduced-order Model for Fluid Flows via Neural Ord…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
Accurate and efficient modeling of cardiac blood flow is crucial for advancing data-driven tools in cardiovascular research and clinical applications. Recently, the accuracy and availability of computational fluid dynamics (CFD)…
The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…
Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves.…
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution,…
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…
We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods,…
Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring…
Reduced order models are becoming increasingly important for rendering complex and multiscale spatio-temporal dynamics computationally tractable. The computational efficiency of such surrogate models is especially important for design,…
Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on…
We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the…
We present a model reduction approach for the real-time solution of time-dependent nonlinear partial differential equations (PDEs) with parametric dependencies. The approach integrates several ingredients to develop efficient and accurate…
Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably…
Much recent interest has focused on the design of optimization algorithms from the discretization of an associated optimization flow, i.e., a system of differential equations (ODEs) whose trajectories solve an associated optimization…
Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…
We explore a reduced-order model (ROM) of plane Couette flow with a view to performing turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier-Stokes (NS) system onto a basis composed of…
In this work, a novel method with an adaptive functional basis for reduced order models (ROM) based on proper orthogonal decomposition (POD) is introduced. The method is intended to be applied in particular to hydrocarbon reservoir…
Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact…
The paper presents a Projection-Based Reduced-Order Model for simulations of high Reynolds turbulent flows. The PBROM are enhanced by incorporating various models of turbulent viscosity and residual closures to model the effects of…