New Trends in Numerical Multiscale Methods and Beyond (Web)

This workshop brings together experts that work on various aspects of numerical multiscale methods and related areas. In the past few years, the field of multiscale methods, i.e. the numerical treatment of phenomena that involve a wide range of vitally different space and time scales, has gone through an enormous transition. With this, the efficiency and reliability of multiscale methods, as well as its range of applications, were significantly improved. At the occasion of this event we want to take the next step by finding and establishing new links to emerging disciplines in the fields of model order reduction and data sciences. For instance, we want to investigate how to improve existing multiscale approaches by replacing or compressing the underlying models (on one or several scales) by using reduced basis strategies. Another possibility is to explore the potential of machine learning strategies, such as designing suitable auto-encoder-decoders, to identify unknown coarse variables or hidden dynamics in a model. This would help design new efficient strategies that enable us to solve problems that cannot be handled with existing schemes. Bridging multiscale schemes with the crucial domain of inverse problems is also vital for many applications ranging from geoscience to medicine. The interplay between statistical tools such as Bayesian or filtering techniques with multiscale modeling has shown some early success but is still in its infancy. In order to achieve these goals, it is crucial to start with gathering experts from the various fields and to present and discuss their relations to multiscale methods. In order to make the conference a fruitful environment for discovering new possibilities, the scope of this workshop is broad and includes multiscale methods based on analytical homogenization theory, heterogenous multiscale methods that do not require scale separation, model order reduction techniques, multiscale machine learning, stochastic homogenization methods as well as statistics and approaches that focus on specific advanced applications.