Implicit and Unified Features
One of the methods to overcoming the scaling problem is to use implicit features. Implicit features are not explicitly defined but are learned from the data. Learned implicit features (called “embeddings”) can scale with number of different chemical species much more efficiently compared to explicit features. However, ML process involving implicit features are usually slower since the model is usually more complex.
Embeddings¶
- Graph Neural Networks (GNNs): GNNs are a natural choice for MLPs because they can naturally represent the local atomic environment as a graph. Examples includes: NequIP, and MACE.
- Deep Neural Networks (DNNs): DNN can be used to construct local environment as embedding vectors based on atomic distances, angles, and types. The weights of the DNN can be trained during fitting. An example is DeepMD
Unified Features¶
You can also combine explicit and implicit features to get the best of both worlds. The idea is to use explicit features to capture the local atomic environment and then use a GNN or DNN to learn the potential energy surface from the explicit features. This approach can improve the accuracy and efficiency of MLPs. Examples includes: SchNet, PhysNet, GemNet, NequIP, and MACE.
- Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J. P., Kornbluth, M., Molinari, N., Smidt, T. E., & Kozinsky, B. (2022). E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature Communications, 13(1). 10.1038/s41467-022-29939-5
- Batatia, I., Kovács, D. P., Simm, G. N. C., Ortner, C., & Csányi, G. (2022). MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields. arXiv. 10.48550/ARXIV.2206.07697
- Zhang, L., Han, J., Wang, H., Car, R., & E, W. (2018). Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics. Physical Review Letters, 120(14). 10.1103/physrevlett.120.143001
- Schütt, K. T., Kindermans, P.-J., Sauceda, H. E., Chmiela, S., Tkatchenko, A., & Müller, K.-R. (2017). SchNet: A continuous-filter convolutional neural network for modeling quantum interactions. 10.48550/ARXIV.1706.08566
- Unke, O. T., & Meuwly, M. (2019). PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges. Journal of Chemical Theory and Computation, 15(6), 3678–3693. 10.1021/acs.jctc.9b00181
- Gasteiger, J., Becker, F., & Günnemann, S. (2021). GemNet: Universal Directional Graph Neural Networks for Molecules. arXiv. 10.48550/ARXIV.2106.08903