# ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations

arXiv: https://arxiv.org/abs/2103.01436 · HTML: https://mlsanity.com/paper/2103.01436/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 2 Mar 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [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)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Searching for Activation Functions](https://mlsanity.com/paper/1710.05941/) (2017)
- [GNN-FiLM: Graph Neural Networks with Feature-wise Linear Modulation](https://mlsanity.com/paper/1906.12192/) (2019)
- [An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storage](https://mlsanity.com/paper/2010.09435/) (2020)
- [Alchemy: A Quantum Chemistry Dataset for Benchmarking AI Models](https://mlsanity.com/paper/1906.09427/) (2019)

## Built on by (most cited first, 30 of 58)

- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalysts](https://mlsanity.com/paper/2206.08917/) (2022)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs](https://mlsanity.com/paper/2206.08515/) (2022)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasets](https://mlsanity.com/paper/2204.02782/) (2022)
- [Position: Graph Learning Will Lose Relevance Due To Poor Benchmarks](https://mlsanity.com/paper/2502.14546/) (2025)
- [Rotation Invariant Graph Neural Networks using Spin Convolutions](https://mlsanity.com/paper/2106.09575/) (2021)
- [Spherical Channels for Modeling Atomic Interactions](https://mlsanity.com/paper/2206.14331/) (2022)
- [Simple GNN Regularisation for 3D Molecular Property Prediction & Beyond](https://mlsanity.com/paper/2106.07971/) (2021)
- [Smooth, exact rotational symmetrization for deep learning on point clouds](https://mlsanity.com/paper/2305.19302/) (2023)
- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [Thermodynamics-informed graph neural networks](https://mlsanity.com/paper/2203.01874/) (2022)
- [A Survey of Generative AI for de novo Drug Design: New Frontiers in Molecule and Protein Generation](https://mlsanity.com/paper/2402.08703/) (2024)
- [Towards Training Billion Parameter Graph Neural Networks for Atomic Simulations](https://mlsanity.com/paper/2203.09697/) (2022)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Grounding Graph Network Simulators using Physical Sensor Observations](https://mlsanity.com/paper/2302.11864/) (2023)
- [Relaxed Equivariance via Multitask Learning](https://mlsanity.com/paper/2410.17878/) (2024)
- [Fast Quantum Property Prediction via Deeper 2D and 3D Graph Networks](https://mlsanity.com/paper/2106.08551/) (2021)
- [Data efficiency and extrapolation trends in neural network interatomic potentials](https://mlsanity.com/paper/2302.05823/) (2023)
- [AI-driven inverse design of materials: Past, present and future](https://mlsanity.com/paper/2411.09429/) (2024)
- [How simple can you go? An off-the-shelf transformer approach to molecular dynamics](https://mlsanity.com/paper/2503.01431/) (2025)
- [Learned Force Fields Are Ready For Ground State Catalyst Discovery](https://mlsanity.com/paper/2209.12466/) (2022)
- [Stability-Aware Training of Machine Learning Force Fields with Differentiable Boltzmann Estimators](https://mlsanity.com/paper/2402.13984/) (2024)

## Abstract (arXiv)

With massive amounts of atomic simulation data available, there is a huge opportunity to develop fast and accurate machine learning models to approximate expensive physics-based calculations. The key quantity to estimate is atomic forces, where the state-of-the-art Graph Neural Networks (GNNs) explicitly enforce basic physical constraints such as rotation-covariance. However, to strictly satisfy the physical constraints, existing models have to make tradeoffs between computational efficiency and model expressiveness. Here we explore an alternative approach. By not imposing explicit physical constraints, we can flexibly design expressive models while maintaining their computational efficiency. Physical constraints are implicitly imposed by training the models using physics-based data augmentation. To evaluate the approach, we carefully design a scalable and expressive GNN model, ForceNet, and apply it to OC20 (Chanussot et al., 2020), an unprecedentedly-large dataset of quantum physics calculations. Our proposed ForceNet is able to predict atomic forces more accurately than state-of-the-art physics-based GNNs while being faster both in training and inference. Overall, our promising and counter-intuitive results open up an exciting avenue for future research.