Related papers: Operator Inference and Physics-Informed Learning o…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…
Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…
We consider the two-phase dynamics of two incompressible and immiscible fluids. As a mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the class of diffuse-interface models. Solutions of the…
We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven…
Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…
This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes…
The present paper develops a reduced-order model capable of modeling unsteady aerodynamic loads in the transonic regime using system identification techniques. The computational fluid dynamics (CFD) calculations are based on the Euler…
Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible…
In this paper, we address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier-Stokes equations. The complexity is quantified by the…
This article considers the problem of reconstructing unknown driving forces based on incomplete knowledge of the system and its state. This is studied in both a linear and nonlinear setting that is paradigmatic in geophysical fluid dynamics…
Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box.…
We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier--Stokes equations. Our model problem is…
In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…
Reduced-order models (ROMs) of turbulent flows based on Galerkin projection often require many degrees of freedom to resolve the dynamics of the turbulence, or simulation data to obtain an optimal modal basis. However, obtaining simulation…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the…
In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…
The identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain data set, but generally approximate the input-output behavior…