Student: Maria Radova
Supervisors: Albert Bartok-Partay; Reinhard J. Maurer

Summary:
In this project the wider applicability of graph neural networks will be explored, to answer questions as "How do atoms arrange in space to form molecules and materials?" and "How does power flow in an electrical grid?". The common theme is that both problems may be represented as graphs: atoms or substations as the vertices, and bonds or transmission lines as the edges. GNNs will be employed to model interactions in such systems and to optimise processes. Results of this work will be useful in optimising electricity grid operations and schedules as well as in understanding chemical transitions between different molecules.

Background:
Atomic systems and electrical power distribution networks may appear to have little in common, but both are challenging to model, and both can be described as graphs, and this project will apply graph neural network techniques to model these systems accurately and computationally efficiently. In case of power grids, direct optimisation of power flow is computationally demanding, therefore surrogate models can help speed up the calculations. Exploiting the graph topology using neural networks can provide accurate predictors for the Hessian preconditioner, which is used to accelerate the optimisation process.

Atomic systems are characterised by connections, or bonds, between the constituent atoms, mapping to the concept of graphs, therefore making the representation by graph neural networks appealing. To elucidate topology and more specifically, the three-dimensional structure of atomic systems, we need to predict the edges or links in the graph. Link prediction using graph neural networks has been suggested[1], and this project would explore adapting this methodology on atomic systems.

Another aspect of graph neural networks is the possibility of embedding triangles[2], or higher than two-body correlations. In atomic systems it is well known that many-body interactions are significant, and it would be interesting to explore connections with power grid networks. In partnership with Invenia Labs [3], we plan to use the predicted Hessian information to accelerate geometry optimisation and transition state search in atomic systems in parallel with optimisation problems in power networks.

References:

[1] https://papers.nips.cc/paper/2018/hash/53f0d7c537d99b3824f0f99d62ea2428-Abstract.html

[2] https://ieeexplore.ieee.org/abstract/document/9377750

[3] https://www.invenia.ca/labs/