Prof. Dr. Alexander Heinlein, Numerical Analysis Group, TU Delft, The Netherlands

Title: Domain decomposition for neural networks

Abstract:

Scientific machine learning (SciML) is a rapidly evolving research field that combines techniques from scientific computing and machine learning. This talk focuses on the application of domain decomposition methods to design neural network architectures and enhance neural network training. In particular, it first explores how domain decomposition techniques can be employed in neural network-based discretizations that can address forward and inverse problems involving partial differential equations, using physics-informed neural networks (PINNs) as well as neural operators. It further discusses domain decomposition-based neural networks and preconditioning strategies for randomized neural networks, where the resulting optimization problem becomes linear in both data-driven settings and PINNs involving linear differential operators. Finally, the talk explores the use of domain decomposition methods for traditional machine learning tasks, such as semantic image segmentation with convolutional neural networks (CNNs). Computational results show that domain decomposition methods can improve efficiency—both in terms of time and memory—as well as enhance accuracy and robustness.

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