Periodic Reporting for period 1 - ARIA (Accurate Roms for Industrial Applications)
Okres sprawozdawczy: 2019-12-01 do 2022-11-30
Reduced-order models (ROMs) are simplified mathematical models derived from the full set of partial differential equations governing the physics of the phenomenon of interest. We study ROMs that are data-driven as they are based on relevant solution data previously obtained by numerical simulations. With ROMs one trades accuracy for speed and scalability of approximate solutions, and counteracts the curse of dimension by significantly reducing the computational complexity. ROMs represent an ideal building block of systems with real-time requirements, like interactive decision support systems that offer the possibility to rapidly explore various alternatives. For that reason, ROMs are receiving high attention by industrial end-users, e.g. for applications like interactive aerodynamic vehicle design, real-time operational optimization of wind farms, and the optimization of medical devices for patient-specific therapies.New approaches have been investigated so far with a focus on the Navier–Stokes equations of fluid flows, one of the most challenging continuum models. Accordingly, we have organized our research activities around the following key objectives: i) advance the state-of-the-art in projection-based ROMs; ii) enhance data-driven modeling via data-geometry inference tools, non-linear linear interpolation, adaptive sampling; iii) integrate ROMs into a multi-fidelity model chain using rigorous error indicators and assess performance in cases of industrial and applicative interest.
All partners in the consortium contributed according to the work plan to achieve the objectives. One new partner supplemented the consortium in order to ensure continuity of modeling expertise because a researcher involved in the project moved. The results achieved so far are in line with expectations.
From the theoretical view point, we have provided among the first advanced analysis of stability and accuracy of ROMs for large eddy simulation (LES) of convection-dominated laminar and transient flows. Furthermore, we have studied turbulence ROMs for numerical stability, error estimates, convergence rates of dynamic sub-scale models. From the view point of data base generation, we have studied new data sampling paradigms that allow increased accuracy of ROMs. We have conceived new clustering and classification approaches of sampled solutions in parameter space. In addition, new interpolation techniques for data augmentation have been proposed based on optimal transportation.
Together with our industrial partners we have investigated ROM based on residual minimization for automotive vehicle aerodynamics with geometric parametrization, with the purpose to industrialize the previously developed multifidelity approach involving active subspaces. We are putting the basis for creating a ROM framework for the simulation of realistic flows and in clinical practice. We have conceived a generative algorithm for synthetic aneurysms geometries that will be uses for building and validating ROMs of realistic vascular flows. The work on theses subjects is ongoing.
From the theoretical view point, we have provided among the first advanced analysis of stability and accuracy of ROMs for large eddy simulation (LES) of convection-dominated laminar and transient flows. Furthermore, we have studied turbulence ROMs for numerical stability, error estimates, convergence rates of dynamic sub-scale models. From the view point of data base generation, we have studied new data sampling paradigms that allow increased accuracy of ROMs. We have conceived new clustering and classification approaches of sampled solutions in parameter space. In addition, new interpolation techniques for data augmentation have been proposed based on optimal transportation.
Together with our industrial partners we have investigated ROM based on residual minimization for automotive vehicle aerodynamics with geometric parametrization, with the purpose to industrialize the previously developed multifidelity approach involving active subspaces. We are putting the basis for creating a ROM framework for the simulation of realistic flows and in clinical practice. We have conceived a generative algorithm for synthetic aneurysms geometries that will be uses for building and validating ROMs of realistic vascular flows. The work on theses subjects is ongoing.
The problem of making intrusive or nonintrusive reduced models is essentially divided into three steps: i) efficient sampling the parameter space; ii) determining from the sampling a global or local reduced basis that is robust with respect to parameter variation; iii) devising a robust interpolation method, for the nonintrusive case, or a stable projection-based numerical scheme in the intrusive case.
For each of these steps the project partners contributed as summarized in the job description. In particular, papers written as a result of the ARIA project and published in leading journals have advanced the limits of knowledge in what concerns reduced model stabilization methods, parameter space sampling techniques, solution mapping techniques, hybrid modeling methods based on domain decomposition, and industrial applications.
Key advantage of model order reduction based on these new contributions are that they will allow engineers to perform simulations and analyses of complex systems more quickly and efficiently, which can lead to significant cost and time savings. For example, in the automotive industry, model order reduction can be used to optimize the design of vehicles by enabling engineers to quickly and accurately simulate and analyze the performance of different design options. In the aerospace industry, model order reduction can be used to analyze the dynamic behavior of aircraft and improve the performance and safety of flight systems.
Overall, the industrial relevance of the new model order reduction paradigms we develop lies in its ability to enable the efficient design and analysis of complex systems, which can lead to improved performance and cost savings in a variety of industries.
This new model order reduction paradigm can also be used to improve the performance of control systems by identifying the key dynamics that need to be controlled, and by reducing the number of control inputs and outputs required to achieve a desired level of performance. This can lead to more efficient and effective control strategies, which can have significant benefits in terms of cost and performance.
For each of these steps the project partners contributed as summarized in the job description. In particular, papers written as a result of the ARIA project and published in leading journals have advanced the limits of knowledge in what concerns reduced model stabilization methods, parameter space sampling techniques, solution mapping techniques, hybrid modeling methods based on domain decomposition, and industrial applications.
Key advantage of model order reduction based on these new contributions are that they will allow engineers to perform simulations and analyses of complex systems more quickly and efficiently, which can lead to significant cost and time savings. For example, in the automotive industry, model order reduction can be used to optimize the design of vehicles by enabling engineers to quickly and accurately simulate and analyze the performance of different design options. In the aerospace industry, model order reduction can be used to analyze the dynamic behavior of aircraft and improve the performance and safety of flight systems.
Overall, the industrial relevance of the new model order reduction paradigms we develop lies in its ability to enable the efficient design and analysis of complex systems, which can lead to improved performance and cost savings in a variety of industries.
This new model order reduction paradigm can also be used to improve the performance of control systems by identifying the key dynamics that need to be controlled, and by reducing the number of control inputs and outputs required to achieve a desired level of performance. This can lead to more efficient and effective control strategies, which can have significant benefits in terms of cost and performance.