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Vector Foundation Project 2024

The project “Wo 1+1 mehr als 2 ist: Kombination von Numerischen Methoden und Maschinellem Lernen” is funded by the Vector Foundation in 2024.

Aims and Objectives

A new approach for solving parametric partial differential equations is to be developed and demonstrated in the project. It is based on combining the numerical Treffz method with deep-learning approaches. The internal approach functions of the Treffz method are replaced by pre-trained neural networks. This makes it possible to achieve a compromise between the effort required to train the networks and a fast numerical simulation of the problem. The application is image reconstruction in ultrasound tomography for breast cancer screening.