On the equivalence of molecular graph convolution and molecular wave function with poor basis set
This work addresses the challenge of reliable and practical material discovery by improving molecular energy prediction through a physics-informed machine learning model, though it appears incremental as it builds on existing quantum and graph-based methods.
The study demonstrates that molecular graph convolutional networks (GCNs) are equivalent to a quantum physics approximation with poor basis sets, and proposes a quantum deep field (QDF) model based on density functional theory for molecular energy prediction, achieving high extrapolation performance when trained on small molecules and tested on large ones.
In this study, we demonstrate that the linear combination of atomic orbitals (LCAO), an approximation of quantum physics introduced by Pauling and Lennard-Jones in the 1920s, corresponds to graph convolutional networks (GCNs) for molecules. However, GCNs involve unnecessary nonlinearity and deep architecture. We also verify that molecular GCNs are based on a poor basis function set compared with the standard one used in theoretical calculations or quantum chemical simulations. From these observations, we describe the quantum deep field (QDF), a machine learning (ML) model based on an underlying quantum physics, in particular the density functional theory (DFT). We believe that the QDF model can be easily understood because it can be regarded as a single linear layer GCN. Moreover, it uses two vanilla feedforward neural networks to learn an energy functional and a Hohenberg--Kohn map that have nonlinearities inherent in quantum physics and the DFT. For molecular energy prediction tasks, we demonstrated the viability of an ``extrapolation,'' in which we trained a QDF model with small molecules, tested it with large molecules, and achieved high extrapolation performance. This will lead to reliable and practical applications for discovering effective materials. The implementation is available at https://github.com/masashitsubaki/QuantumDeepField_molecule.