Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. In this context, this talks focuses on the enhancement of machine learning using classical numerical methods, in particular, on improving neural networks using domain decomposition-inspired architectures. In the first part of this talk, the domain decomposition paradigm is applied to the approximation of the solutions of partial differential equations (PDEs) using physics-informed neural networks (PINNs). It is observed that network architectures inspired by multi-level Schwarz domain decomposition methods can improve the performance for certain challenging problems, such as multiscale problems. This part of the talk is based on joint work with Victorita Dolean (University of Strathclyde, Côte d’Azur University), Siddhartha Mishra, and Ben Moseley (ETH Zürich). Moreover, a classical machine learning task is considered, that is, image segmentation using convolutional neural networks (CNNs). Domain decomposition techniques offer a way of scaling up common CNN architectures, such as the U-Net. In particular, local subdomain networks learn local features and are coupled via a coarse network which incorporates global features. The second part of this talk is based on joint work with Eric Cyr (Sandia National Laboratories)and Corné Verburg (Delft University of Technology).