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Model order reduction of transport-dominated systems with rotations using shifted proper orthogonal decomposition and artificial neural networks
Kovárnová, A. ; Isoz, Martin
In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction (MOR) of such systems, the shifted proper orthogonal decomposition with interpolation via artificial neural networks, is further extended by improving the handling of general transport operators. First, even with intrusive MOR approaches, the underlying numerical solvers can provide only discrete realizations of transports linked to the movement of individual particles in the system. On the other hand, our MOR methodology requires continuous transport operators. Thus, the original framework was extended by the possibility to reconstruct continuous approximations of known discrete transports via another artificial neural network. Second, the treatment of rotation-comprising transports was significantly improved.
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Model order reduction for particle-laden flows: systems with rotations and discrete transport operators
Kovárnová, A. ; Isoz, Martin
In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction (MOR) of such systems, the shifted proper orthogonal decomposition with interpolation via artificial neural networks, is further extended by improving the handling of general transport operators. First, even with intrusive MOR approaches, the underlying numerical solvers can provide only discrete realizations of transports linked to the movement of individual particles in the system. On the other hand, our MOR methodology requires continuous transport operators. Thus, the original framework was extended by the possibility to reconstruct continuous approximations of known discrete transports via another artificial neural network. Second, the treatment of rotation-comprising transports was significantly improved.
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Shifted proper orthogonal decomposition and artificial neural networks for time-continuous reduced order models of transport-dominated systems
Kovárnová, A. ; Krah, P. ; Reiss, J. ; Isoz, Martin
Transport-dominated systems are pervasive in both industrial and scientific applications. However, they provide a challenge for common mode-based model order reduction (MOR) approaches, as they often require a large number of linear modes to obtain a sufficiently accurate reduced order model (ROM). In this work, we utilize the shifted proper orthogonal decomposition (sPOD), a methodology tailored for MOR of transport-dominated systems, and combine it with an interpolation based on artificial neural networks (ANN) to obtain a time-continuous ROM usable in engineering practice. The resulting MOR framework is purely data-driven, i.e., it does not require any information on the full order model (FOM) structure, which extends its applicability. On the other hand, compared to the standard projection-based approaches to MOR, the dimensionality reduction utilizing sPOD and ANN is significantly more computationally expensive since it requires a solution of high-dimensional optimization problems.
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