Related papers: Deep learning-based reduced-order methods for fast…
Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…
The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…
This paper introduces a novel data-driven convergence booster that not only accelerates convergence but also stabilizes solutions in cases where obtaining a steady-state solution is otherwise challenging. The method constructs a…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Deep Learning-based Reduced Order Models (DL-ROMs) provide nowadays a well-established class of accurate surrogate models for complex physical systems described by parametrized PDEs, by nonlinearly compressing the solution manifold into a…
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…
This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called "reduced-order model" (ROM) is obtained from reduction of the…
Time-dependent partial differential equations (PDEs) for classic physical systems are established based on the conservation of mass, momentum, and energy, which are ubiquitous in scientific and engineering applications. These PDEs are…
The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…
The numerical simulation of electromagnetic transients in fusion devices is essential for analyzing plasma stability and disruptive events. However, it remains computationally demanding due to the large-scale dense systems arising from…
This paper presents a projection-based reduced order modelling (ROM) framework for unsteady parametrized optimal control problems (OCP$_{(\mu)}$s) arising from cardiovascular (CV) applications. In real-life scenarios, accurately defining…
In this paper, we propose a domain-decomposition-based deep learning (DL) framework, named transient-CoMLSim, for accurately modeling unsteady and nonlinear partial differential equations (PDEs). The framework consists of two key…
Proper orthogonal decomposition (POD) is often employed in developing reduced-order models (ROM) in fluid flows for design, control, and optimization. Contrary to the usual practice where velocity field is the focus, we apply the POD…
In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…
Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…
The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…
Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM)…
Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a…
The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…
In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…