Related papers: On snapshot-based model reduction under compatibil…
The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in…
This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction…
Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…
We discuss structure-preserving model order reduction for port-Hamiltonian systems based on an approximation of the full-order state by a linear combination of ansatz functions which depend themselves on the state of the reduced-order…
Flow models transform data gradually from one modality (e.g. noise) onto another (e.g. images). Such models are parameterized by a time-dependent velocity field, trained to fit segments connecting pairs of source and target points. When the…
In this paper, we present a new self-supervised scene flow estimation approach for a pair of consecutive point clouds. The key idea of our approach is to represent discrete point clouds as continuous probability density functions using…
In this study, we analyze the flow filtration process of slightly compressible fluids in fractured porous media. We model the coupled fractured porous media system, where the linear Darcy flow is considered in porous media and the nonlinear…
Surrogate models have shown to be an extremely efficient aid in solving engineering problems that require repeated evaluations of an expensive computational model. They are built by sparsely evaluating the costly original model and have…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…
Addressing challenges in urban water infrastructure systems including aging infrastructure, supply uncertainty, extreme events, and security threats, depend highly on water distribution networks modeling emphasizing the importance of…
We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…
We introduce a theoretical and numerical method to investigate the properties of electro-osmotic flows under conditions of extreme confinement. The present approach, aiming to provide a simple modeling of electrolyte solutions described as…
Diffusion and flow-matching have emerged as powerful methodologies for generative modeling, with remarkable success in capturing complex data distributions and enabling flexible guidance at inference time. Many downstream applications,…
Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…
In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinley parametrized geometries. The essential ingredients of the methodology are: a Galerkin…
We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…
An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity of temporal scales. A novel…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…