MS403 Reduced order modeling strategies for parametrized PDEs

undefinedG. Rozza1, K. Veroy Grepl2


This proposed minisymposium will consider a range of model reduction strategies with applications in real-time computing. The increasing complexity of mathematical models used to predict real-world systems, such as the climate or the human cardiovascular system, has lead to a need for model reduction techniques. Such techniques develop systematic algorithms for substituting complex models with ones that are far simpler but nevertheless accurately capture the most important aspects of the phenomena being modeled. Some subtopics include state space and parameter space reduction -- with a special emphasis on reduced basis methods and proper orthogonal decomposition. The minisymposium will emphasize model reduction topics in several themes:


  1. design, optimization, and control theory in real-time with applications in engineering; 
  2. data assimilation, geometry registration, and parameter estimation with a special attention to real-time computing in biomedical engineering and computational physics; 
  3. real-time visualization of physics-based simulations in computer science; 
  4. the treatment of high-dimensional problems in state space, physical space, or parameter space; 
  5. the interactions between different model reduction and dimensionality reduction approaches; 
  6. the development of general error estimation frameworks which accomodate both model and discretization effects.


A strong attention is on mathematical models based on parametrized ordinary and partial differential equations. We will emphasize engineering and life-sciences applications, including continuum mechanics, fluid dynamics, and transport problems. Other mathematical frameworks and application domains may also be considered to provide perspective and opportunity for "technology transfer" and interdisciplinary exchanges. However, even if the focus of the minisymposium is methodological, we expect a wide range of both academic and industrial problems of high complexity to motivate, stimulate, and ultimately demonstrate the meaningfulness and efficiency of the proposed approaches. The emphasis on real-time computing applications, and above all real-time visualization, can be seen as a new frontier in scientific computing to assist scientists and engineers during design, construction, manufacturing or production phases, and even medical doctors during surgery or diagnosis. Reduced order modelling has found a wide range of applications in several areas in science and computational engineering, and its increasing popularity is underscored by the many minisymposia at conferences such as ICOSAHOM, ECCOMAS CFD, SIAM CSE and ICIAM in the last few years.


The aim of this minisymposium is to discuss successful developments, to address current challenges, and to identify new directions. The objectives of the minisymposium are focused on a strong interaction and integration of several contributions on model order reduction developed in the last few years in diff erent fields and with different purposes.


The goals are: 

  1. To have a strong dialogue between scientists doing research on model order reduction for ordinary and partial differential equations. 
  2. To extend the state of the art in model reduction into the possibility of performing real-time computing (needs, applications). 
  3. To open a discussion about real-time visualization techniques in many fields ranging from physics-based animation to virtual surgery. 
  4. To further advance the discussion about reliability of reduced order models compared with classical discretization techniques and methodologies. 
  5. To extend the state of the art concerning parametrization techniques from a physical and geometrical point of view, in order to better deal with realistic geometries and complex systems. 
  6. To extend the state of the art related with the need of novel sampling and parameter space exploration techniques.


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