Related papers: A Nonintrusive Distributed Reduced Order Modeling …

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…

Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…

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…

We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…

This work presents a method to adaptively refine reduced-order models \emph{a posteriori} without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive $h$-refinement: it enriches the reduced-basis space…

We develop a unified framework for the design and analysis of high-order nonconforming virtual element methods for nonlinear fourth-order reaction--diffusion problems in two dimensions, with emphasis on clamped, Navier, and…

Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…

This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our…

We propose a general dynamic reduced-order modeling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved PIV snapshots. This framework contains four steps. First, the sensor signals are lifted to…

We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…

We analyze the performance of a reduced-order simulation of geometric meta-materials based on zigzag patterns using a simplified representation. As geometric meta-materials we denote planar cellular structures which can be fabricated in 2d…

This study presents a comprehensive theoretical framework to simulate the response of multiscale nonlocal elastic beams. By employing distributed-order (DO) fractional operators with a fourth-order tensor as the strength-function, the…

This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…

We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…

This paper presents a novel derivation of the direct parametrisation method for invariant manifolds able to build simulation-free reduced-order models for nonlinear piezoelectric structures, with a particular emphasis on applications to…

In the current era of vast data and transparent machine learning, it is essential for techniques to operate at a large scale while providing a clear mathematical comprehension of the internal workings of the method. Although there already…

Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality…