Related papers: Verifiability of the Data-Driven Variational Multi…

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

In our earlier work, we proposed a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows, which can be formally written as \begin{equation*} \boxed{ \text{ DDF-ROM = Galerkin-ROM +…

This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method…

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

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…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Waveform inversion is concerned with estimating a heterogeneous medium, modeled by variable coefficients of wave equations, using sources that emit probing signals and receivers that record the generated waves. It is an old and intensively…

Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…

Suitable reduced order models (ROMs) are computationally efficient tools in characterizing key dynamical and statistical features of nature. In this paper, a systematic multiscale stochastic ROM framework is developed for complex systems…

This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are…

This paper explores how to identify a reduced order model (ROM) from a physical system. A ROM captures an invariant subset of the observed dynamics. We find that there are four ways a physical system can be related to a mathematical model:…

This paper develops a direct data-driven framework for constructing reduced-order models (ROMs) of discrete-time linear dynamical systems with unknown dynamics and process disturbances. The proposed scheme enables controller synthesis on…

We develop a Reduced Order Model (ROM) for a Large Eddy Simulation (LES) approach that combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies…

Computational physics simulation can be a powerful tool to accelerate industry deployment of new scientific technologies. However, it must address the challenge of computationally tractable, moderately accurate prediction at large industry…

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators'…

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

This paper investigates the recently introduced data-driven correction reduced order model (DDC-ROM) in the numerical simulation of the quasi-geostrophic equations. The DDC-ROM uses available data to model the correction term that is…

Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced…

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…

In course of this work, we examine the process of plastic profile extrusion, where a polymer melt is shaped inside the so-called extrusion die and fixed in its shape by solidification in the downstream calibration unit. More precise, we…