Related papers: StabOp: A Data-Driven Stabilization Operator for R…
This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced…
We developed a novel reduced-order multi-scale method for solving large time-domain wavefield simulation problems. Our algorithm consists of two main stages. During the first "off-line" stage the fine-grid operator (of the graph Laplacian…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…
Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…
Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and…
Reduced-order models (ROMs) are very popular for surrogate modeling of full-order computational fluid dynamics (CFD) simulations, allowing for real-time approximation of complex flow phenomena. However, their application to CFD models…
We develop an on-the-fly reduced-order model (ROM) integrated with a flow simulation, gradually replacing a corresponding full-order model (FOM) of a physics solver. Unlike offline methods requiring a separate FOM-only simulation prior to…
We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to…
Parametric data-driven reduced-order models (ROMs) that embed dependencies in a large number of input parameters are crucial for enabling many-query tasks in large-scale problems. These tasks, including design optimization, control, and…
Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…
Scale-resolving flow simulations often feature several million [thousand] spatial [temporal] discrete degrees of freedom. When storing or re-using these data, e.g., to subsequently train some sort of data-based surrogate or compute…
Reduced-order models (ROMs) are essential for rapid simulation of complex biomechanical systems and for bridging the gap between high fidelity models and clinical application. However, ROMs for tissue growth and remodeling (G&R) remain…
For reduced order models (ROMs) of fluid flows, we investigate theoretically and computationally whether differentiation and ROM spatial filtering commute, i.e., whether the commutation error (CE) is nonzero. We study the CE for the…
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…
In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM)…
Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…
For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based…