Inverse Problems in Designing New Structural Materials

The development of new structural materials with desirable properties has become one of the most challenging tasks for engineers. High performance alloys are required for the continued development of cars, aircraft and more complex structures. The vast search space for the parameters needed to design these materials makes all established approaches very expensive and time-consuming. A high-throughput screening method has been recently introduced in which many small samples are produced and exposed to different tests. Properties of the materials are predicted by a so-called predictor function that uses the information extracted from these tests. This approach offers not only a quick and cheap exploration of the search space but also the generation of a large data-set containing parameters and predicted material properties. From such a data-set we define a forward operator (Neural Network) mapping from parameters to the material properties and focus mainly on solving the corresponding Inverse Problem: given desired properties a material should have, find the material and production parameters to construct it. We use Tikhonov regularization to reduce the ill-posedness of the problem and a proximal gradient method to find the solution. The main contribution of our work is to exploit an idea from other recent works that incorporate tolerances into the Tikhonov functional.