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Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on…

We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC-AE) has been shown to capture…

Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational…

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…

This article presents an innovative open-source software named ModelFLOWs-app, written in Python, which has been created and tested to generate precise and robust hybrid reduced order models (ROMs) fully data-driven. By integrating modal…

This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy…

The onerous task of repeatedly resolving certain parametrized partial differential equations (pPDEs) in, e.g. the optimization context, makes it imperative to design vastly more efficient numerical solvers without sacrificing any accuracy.…

Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…

The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…

This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

It is of great interest to solve the inverse problem of stationary radiative transport equation (RTE) in optical tomography. The standard way is to formulate the inverse problem into an optimization problem, but the bottleneck is that one…

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

We present a reduced-order model (ROM) methodology for inverse scattering problems in which the reduced-order models are data-driven, i.e. they are constructed directly from data gathered by sensors. Moreover, the entries of the ROM contain…

Machine learning and artificial intelligence algorithms typically require large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden…

Reduced-order models (ROMs) that capture changes in fluid systems due to variations in parameters, such as the Reynolds number or the shape of a stationary body placed in the flow, are attracting increasing attention in engineering…

We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the…

Partial differential equations (PDEs) are widely used for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or the solution of the…