FT4 Numerical optimization based on predictive models
Prof. Michael Stingl
Applied Mathematics II
Cluster of Excellence
Engineering of Advanced Materials
The ultimate goal in advanced materials design is to determine structures with desired properties and related processes that lead to this structure. Unlike in standard engineering setups, where one concludes from a known set of process parameters to resulting structures and from the latter to associated properties, the idea is to systematically invert this process. For this purpose, a desired design property is expressed in terms of a mathematical function, the so-called objective-function. The objective-function establishes a link from the desired material property to parameters characterizing the underlying processes and structures by means of structure- property and process-structure relations. The key challenge is to provide precisely these relations in a validated and numerically accessible form and to integrate them within a unified optimization framework.
In contrast to trial-and-error approaches, modern optimization techniques allow the identification of a huge set of parameters, which “optimize” the value of a given function for the computational cost of carrying out only a few process and structure simulations. An important condition making these powerful tools work is a – in a mathematical sense – sufficiently rich structure of the underlying functions describing the physical or chemical processes, structures and properties.
Main challenges in FT4 will be to find a reasonable balance between reliability (is the model able to predict the outcome of the process?) and numerical tractability (is it possible to “solve” the model in reasonable time?) as well as to device optimization algorithms robust enough to cope with these models.