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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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Vizuálně realistické modelování deformací dynamických objektů
Bulušek, Petr ; Boldyš, Jiří (vedoucí práce) ; Šír, Zbyněk (oponent)
V předložené práci studujeme metody pro simulování fyziky pevných těles a deformovatelných těles. V první kapitole se dá nalézt řešerše některých přístupů k simulaci pevných těles s důrazem na metodu používanou v open source fyzikálním enginu Bullet. Ve druhé kapitole se dají nalézt nejpoužívanější metody pro simulaci deformací opět s důrazem na fyzikální engine Bullet. Dále je studována možnost, jak redukovat dimenzi rovnic, které vzniknou diskretizací parciálních diferenciálních rovnic elastického tělesa metodou konečných prvků. Redukce je studována na příkladu tělesa tvořeného tyčovými elementy. Powered by TCPDF (www.tcpdf.org)
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CFD motivated applications of model order reduction
Isoz, Martin
The ongoing advances in numerical mathematics and available computing power combined with the industrial needs promote a development of more and more complex models. However, such models are, due to their complexity, expensive from the point of view of the data storage and the time necessary for their evaluation. The model order reduction (MOR) seeks to reduce the computational complexity of large scale models. We present an approach to MOR based on the proper orthogonal decomposition (POD) with Galerkin projection. The problems arising from the nonlinearities present in the original model are adressed within the framework of the discrete empirical interpolation method (DEIM). The main contribution of this work consists in providing a link between the POD-DEIM based MOR and OpenFOAM. OpenFOAM is an open-source CFD toolbox capable of solving even industrial scale processes. Hence, the availability of a link between OpenFOAM and POD-DEIM based MOR enables a direct order reduction for large scale systems originating in the industrial practice.
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Vizuálně realistické modelování deformací dynamických objektů
Bulušek, Petr ; Boldyš, Jiří (vedoucí práce) ; Šír, Zbyněk (oponent)
V předložené práci studujeme metody pro simulování fyziky pevných těles a deformovatelných těles. V první kapitole se dá nalézt řešerše některých přístupů k simulaci pevných těles s důrazem na metodu používanou v open source fyzikálním enginu Bullet. Ve druhé kapitole se dají nalézt nejpoužívanější metody pro simulaci deformací opět s důrazem na fyzikální engine Bullet. Dále je studována možnost, jak redukovat dimenzi rovnic, které vzniknou diskretizací parciálních diferenciálních rovnic elastického tělesa metodou konečných prvků. Redukce je studována na příkladu tělesa tvořeného tyčovými elementy. Powered by TCPDF (www.tcpdf.org)
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