Mixed-integer optimisation of graph neural networks for computer-aided molecular design

Mixed-integer optimisation of graph neural networks for computer-aided molecular design

McDonald, Tom (Student TU Delft)
Tsay, Calvin (Imperial College London)
Schweidtmann, A.M. (TU Delft ChemE/Process Systems Engineering)
Yorke-Smith, N. (TU Delft Algorithmics)

2024

ReLU neural networks have been modelled as constraints in mixed integer linear programming (MILP), enabling surrogate-based optimisation in various domains and efficient solution of machine learning certification problems. However, previous works are mostly limited to MLPs. Graph neural networks (GNNs) can learn from non-euclidean data structures such as molecular structures efficiently and are thus highly relevant to computer-aided molecular design (CAMD). We propose a bilinear formulation for ReLU Graph Convolutional Neural Networks and a MILP formulation for ReLU GraphSAGE models. These formulations enable solving optimisation problems with trained GNNs embedded to global optimality. We apply our optimisation approach to an illustrative CAMD case study where the formulations of the trained GNNs are used to design molecules with optimal boiling points.

Graph neural networks
GraphSAGE
Mixed integer programming
Molecular design
Optimal boiling point

http://resolver.tudelft.nl/uuid:d9904329-087a-4799-8327-e0159a30be88

https://doi.org/10.1016/j.compchemeng.2024.108660

2024-09-22

0098-1354

Computers & Chemical Engineering, 185

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2024 Tom McDonald, Calvin Tsay, A.M. Schweidtmann, N. Yorke-Smith