Related papers: Parametric model order reduction for a wildland fi…
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…
Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear…
In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…
The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
Training of deep neural networks (DNNs) frequently involves optimizing several millions or even billions of parameters. Even with modern computing architectures, the computational expense of DNN training can inhibit, for instance, network…
A proper orthogonal decomposition-based B-splines B\'ezier elements method (POD-BSBEM) is proposed as a non-intrusive reduced-order model for uncertainty propagation analysis for stochastic time-dependent problems. The method uses a…
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…
For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…
Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…
In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper…
High-fidelity simulations of mixing and combustion processes are generally computationally demanding and time-consuming, hindering their wide application in industrial design and optimization. The present study proposes parametric reduced…
This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical…
Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…
We present a framework for optimal trajectory generation in flow-driven systems governed by the Navier-Stokes equations, combining a Proper Orthogonal Decomposition (POD) reduced0order model (ROM) with Model Predictive Control (MPC). The…
The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential Equations (PDEs).…
Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with…
Fluid dynamics systems driven by dominant, nearly periodic large-scale dynamics are common across wakes, jets, rotating machinery, and high-speed flows. Traditional decomposition techniques such as proper orthogonal decomposition and…