Further reading#

The primary literature behind the course, grouped by theme, with the lesson that uses each work. All links are DOIs or arXiv entries.

Core frameworks and foundational methods#

Work	Used in
Geiger & Smidt, e3nn: Euclidean Neural Networks, arXiv:2207.09453 (2022)	throughout
Thomas et al., Tensor Field Networks, arXiv:1802.08219 (2018)	03a, 06a
Weiler et al., 3D Steerable CNNs, NeurIPS (2018)	01b, 06a
Battaglia et al., Relational inductive biases and graph networks, arXiv:1806.01261 (2018)	05a
Fuchs et al., SE(3)-Transformers, NeurIPS (2020)	06a
Anderson et al., Cormorant, NeurIPS (2019)	03a
Liao & Smidt, Equiformer, ICLR (2023)	04
Grisafi et al., Symmetry-adapted machine learning for tensorial properties of atomistic systems, Phys. Rev. Lett. 120 036002 (2018)	background

Work	Used in
Behler & Parrinello, Generalized neural-network representation of high-dimensional potential-energy surfaces, Phys. Rev. Lett. 98 146401 (2007)	05b, 08a
Schütt et al., SchNet: A continuous-filter convolutional neural network for modeling quantum interactions, arXiv:1706.08566 (2017)	07a
Schütt et al., SchNet — A deep learning architecture for molecules and materials, J. Chem. Phys. 148 241722 (2018)	07a
Gasteiger et al., Directional message passing for molecular graphs (DimeNet), arXiv:2003.03123 (2020)	07b
Gasteiger et al., DimeNet++, arXiv:2011.14115 (2022)	07b

Work	Used in
Batzner et al., NequIP, Nat. Commun. 13 2453 (2022)	08a, 08b
Musaelian et al., Allegro, Nat. Commun. 14 579 (2023)	09a, 09b
Batatia et al., MACE, NeurIPS (2022)	10b, 10c
Batatia et al., The design space of E(3)-equivariant potentials, arXiv:2205.06643 (2022) · Nat. Mach. Intell. 7 56 (2025)	10b
Kovács et al., Evaluation of MACE, J. Chem. Phys. 159 044118 (2023)	10c
Kovács et al., MACE-OFF, J. Am. Chem. Soc. 147 17598 (2025)	10c
Batatia et al., MACE-MP-0 foundation model, arXiv:2401.00096 (2024)	11

Work	Used in
Drautz, Atomic cluster expansion, Phys. Rev. B 99 014104 (2019)	10a
Dusson et al., ACE: completeness, efficiency, stability, J. Comput. Phys. 454 110946 (2022)	10a
Nigam et al., Unified theory of atom-centered representations and message passing, J. Chem. Phys. 156 204115 (2022)	10a, 10b
Pozdnyakov & Ceriotti, Incompleteness of GNNs for point clouds, arXiv:2201.07136 (2022)	07b, 10a
Chong et al., Resolving the body-order paradox of MLIPs, J. Chem. Phys. 164 064121 (2026)	10a

Work	Used in
Grisafi & Ceriotti, Incorporating long-range physics, J. Chem. Phys. 151 204105 (2019)	05a
Kosmala et al., Ewald-based message passing, PMLR 202 17544 (2023)	05a
Cheng, Latent Ewald summation, npj Comput. Mater. 11 80 (2025)	05a
Kolafa & Perram, Cutoff errors in Ewald summation, Mol. Simul. 9 351 (1992)	05b

Work	Used in
Chmiela et al., Machine learning of accurate energy-conserving molecular force fields (MD17), Sci. Adv. 3 e1603015 (2017)	07c
Christensen & von Lilienfeld, On the role of gradients for machine learning of molecular energies and forces (rMD17), arXiv:2007.09593 (2020)	07c

e3nn documentation — the API this course teaches
The official e3nn MRS Fall 2021 tutorial — a shorter, complementary walkthrough by the library authors
PyTorch Geometric documentation — graph batching and scatter operations
ASE documentation — structures, calculators, MD
MACE · NequIP · Allegro — the reference implementations of the potentials rebuilt in Part IV