# Domain-informed graph neural networks: a quantum chemistry case study

arXiv: https://arxiv.org/abs/2208.11934 · HTML: https://mlsanity.com/paper/2208.11934/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 25 Aug 2022.

## Builds on (most cited first, 22 of 22)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Spherical Channels for Modeling Atomic Interactions](https://mlsanity.com/paper/2206.14331/) (2022)
- [Graph Neural Networks for Modelling Traffic Participant Interaction](https://mlsanity.com/paper/1903.01254/) (2019)
- [Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data](https://mlsanity.com/paper/1808.04327/) (2018)
- [ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks](https://mlsanity.com/paper/2206.05437/) (2022)
- [Directional Message Passing on Molecular Graphs via Synthetic Coordinates](https://mlsanity.com/paper/2111.04718/) (2021)
- [Molecular Representation Learning via Heterogeneous Motif Graph Neural Networks](https://mlsanity.com/paper/2202.00529/) (2022)
- [PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgery](https://mlsanity.com/paper/2109.04352/) (2021)
- [Knowledge-based Biomedical Data Science 2019](https://mlsanity.com/paper/1910.06710/) (2019)

## Built on by (most cited first, 3 of 3)

- [Towards Complex Dynamic Physics System Simulation with Graph Neural ODEs](https://mlsanity.com/paper/2305.12334/) (2023)
- [SA-GAT-SR: Self-Adaptable Graph Attention Networks with Symbolic Regression for high-fidelity material property prediction](https://mlsanity.com/paper/2505.00625/) (2025)
- [Cascaded Transformer for Robust and Scalable SLA Decomposition via Amortized Optimization](https://mlsanity.com/paper/2601.11859/) (2026)

## Abstract (arXiv)

We explore different strategies to integrate prior domain knowledge into the design of a deep neural network (DNN). We focus on graph neural networks (GNN), with a use case of estimating the potential energy of chemical systems (molecules and crystals) represented as graphs. We integrate two elements of domain knowledge into the design of the GNN to constrain and regularise its learning, towards higher accuracy and generalisation. First, knowledge on the existence of different types of relations (chemical bonds) between atoms is used to modulate the interaction of nodes in the GNN. Second, knowledge of the relevance of some physical quantities is used to constrain the learnt features towards a higher physical relevance using a simple multi-task paradigm. We demonstrate the general applicability of our knowledge integrations by applying them to two architectures that rely on different mechanisms to propagate information between nodes and to update node states.