The MaGriDo consortium, funded by the German Federal Ministry of Education and Research, carried out a three‑year project (2021‑2023) that brought together the Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) and several university groups, including the Technical University of Berlin, the University of Bonn, and the Technical University of Munich. Dr. Jan Hamaekers served as project lead, coordinating the consortium’s activities and ensuring that the allocated resources were used efficiently. The project’s budget was dominated by personnel costs, with a separate financial statement detailing the use of funds. Communication within the consortium was facilitated through email lists, an OwnCloud server, a GitLab repository, and a dedicated website, all hosted by SCAI.

The scientific focus of Part 4 of MaGriDo was the design and implementation of deep graph neural networks for material development, targeting molecules, polymers, and glasses. Three generations of problems were addressed: first‑generation predictive models that infer material properties from atomistic structure, second‑generation models that predict properties from chemical composition, and third‑generation generative models that enable inverse design of structures with desired characteristics. The demonstration application was the prediction of molecular properties on the QM9 benchmark dataset, which required the creation of standardized data formats, interfaces, and shared repositories.

Graph‑convolutional networks (GCNs) were developed for both 3‑D structural inputs and 2‑D SMILES representations. A two‑layer GCN that incorporates atom and bond features achieved prediction accuracies within the desired chemical accuracy for a range of properties, as reported in the consortium’s publications. To capture tensorial observables such as dipole moments, conventional invariant GCNs proved insufficient because they lose relational information between atomic environments. Consequently, equivariant GCNs (EGCNs) were introduced, leveraging moment tensors and Clebsch‑Gordan transformations to preserve rotational symmetry. These EGCNs were successfully applied to approximate Born‑Oppenheimer energy surfaces, providing flexible potential‑energy representations suitable for molecular dynamics simulations. ResNet‑style architectures were also explored and found to improve performance for certain energy‑surface tasks.

Beyond predictive accuracy, the project emphasized the integration of domain knowledge, interpretability, and transfer learning. The University of Bonn contributed work on embedding chemical rules and prior knowledge into the network architecture, while the Technical University of Munich focused on transfer‑learning strategies that allow models trained on one material class to be adapted to another. These efforts are documented in the AP2, AP3, and AP4 work packages, which address expressivity, training, and the incorporation of domain knowledge, respectively.

The outcomes of Part 4 include a suite of graph‑network prototypes and workflow frameworks that can be applied to first‑generation material‑property prediction problems. The developed GCNs and EGCNs have been made available through the consortium’s GitLab repository, enabling other researchers to build upon the work. The project’s results demonstrate that embedding domain knowledge into deep learning architectures yields efficient, interpretable models that perform on par with or better than traditional end‑to‑end approaches, thereby advancing the state of the art in computational materials science.