Product development today is increasingly based on simulation and optimization of virtual products and processes (digital twins) that are described via mathematical models that encode the real physical product/process as well as free parameters that are used in optimization and control. Deeply refined mathematical models are required to understand and simulate the true physical processes, while for control and optimization less refined models need to be employed to handle the complexity. To achieve best performance of mathematical modelling, simulation and optimization (MSO) techniques, in particular in the industrial environment, a complete model hierarchy would be ideal which contains very fine and very coarse models and which can be used both for simulation and optimization on computers in an effective way. The currently most favoured way in industrial applications to achieve such a model hierarchy is to use a sufficiently fine parameterized model and then to use model order reduction (MOR) techniques to tune the fine model to the accuracy, complexity and computational speed in simulation and parameter optimization.

Although the mathematical models differ strongly in applications and industrial sectors, there is a common framework via an appropriate representation of the physical model via equations and functions. The main objective of this programme is to further develop this common framework and, driven by industrial applications from different sectors, to lift mathematical MSO and MOR to a new level of quality and to train the next generation of researchers in this approach. A particular feature of the programme is the treatment of high dimensional and coupled systems that describe different phenomena on different scales. Such systems present a major challenge for simulation and optimization and require new MOR techniques.

The partners are from the academic sector TU Berlin/MATHEON (consortium leader), HU Berlin, U. Bremen, FAU Erlangen-Nürnberg, INRIA Paris,  U. Linz, Polytechnico di Milano, Technological Institute of Industrial Mathematics (ITMATI) Santiago, SISSA Trieste, BU Wuppertal, FAU Erlangen-Nürnberg, as well as 11 industrial partners from 7 countries and the European Network EU-MATHS-IN. (Funds on the order of 2.8 Million Euro).

En el proyecto ROMSOC, ITMATI participa como socio participativo, desarrollando acciones por valor muy próximo a quinientos mil euros, en el que se desarrollarán dos tesis doctorales en el ámbito de la Matemática Industrial, bajo la dirección de los investigadores principales: Dra. Peregrina Quintela Estévez (Investigadora Adscrita y Directora de ITMATI, Catedrática de Matemática Aplicada en la USC) y el Dr. Andrés Prieto Aneiros (Investigador Adscrito a ITMATI y Contratado Doctor en la UDC). Los proyectos de investigación industrial que se desarrollarán son los siguientes:

 
 
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