marcel.science / tasd4mlip
Truncated automatic sparse differentiation for machine learning interatomic potentials
Hello! 👋 This website is a supplement to our preprint (see below) on computing Hessians of machine-learning interatomic potentials with (truncated) automatic sparse differentiation. This is where we collect links to code and data related to the work, and give an overview of the external data we relied on.
Preprint
- Title: Truncated automatic sparse differentiation for machine learning interatomic potentials
- Preprint: arxiv:2609.20510 (2026)
- Abstract: Machine learning interatomic potentials (MLIPs) learn the mapping from atomic positions to potential energy. The forces, the negative gradient of this energy, drive molecular dynamics and are readily obtained using automatic differentiation. Higher-order derivatives, most notably the Hessian, describe collective motion and allow the direct prediction of experimental observables, but are considered computationally inaccessible for large systems. We suggest a solution: in physical systems, interactions decay with distance, and most MLIPs build on this locality through message passing up to a finite receptive field. This implies both sparsity of higher-order derivatives and their decay with distance. This structure can be exploited using automatic sparse differentiation (ASD). We explain how to compute the sparsity pattern for MLIP derivatives and demonstrate that, for multiple foundation MLIPs, ASD computes full Hessians of large porous materials exactly, but with modest speedups at best. The larger gains come from truncated ASD: discarding small, but nonzero, Hessian entries between distant atoms yields order-of-magnitude speedups with negligible impact on predicted observables.
Please contact Marcel for questions about the paper, and Adrian for questions about asdex, the automatic sparse differentiation library this work builds on. You can also say hi on twitter 🐦 marceldotsci or bluesky 🌀 marceldotsci!
Code & Data
All code and data of this work are available in a single archive. It contains a re-implementation of MACE, the asdex wrappers for sparse and dense Hessians, the tooling to get sparsity patterns and more efficient coloring, as well as experiments, analysis, figures, tables, and so on.
doi:10.5281/zenodo.22813524: The archive on Zenodo, as a single zip.tasd4mlip-archive: The same archive, mirrored on GitHub (binary data in LFS).
This is intended as an archive, not as a production implementation of the method. A production-ready implementation of truncated automatic sparse differentiation will be made available in pet-jax. Stay tuned! 🚀
Data sources
The archive documents the provenance of every external input in detail (see its sources/README.md). We mostly rely on the following external data:
- Moosavi et al. (2022): The 233-structure benchmark set of porous materials (214 MOFs, 9 COFs, and 9 zeolites) with DFT reference heat capacities, from A data-science approach to predict the heat capacity of nanoporous materials, Nat. Mater. 21, 1419 (2022), via Materials Cloud (CC BY 4.0).
- Gönnheimer et al. (2025): Reference MACE heat capacities and phonon frequencies for that set, in unit cells and 2×2×2 supercells, from Beyond numerical Hessians: higher-order derivatives for machine learning interatomic potentials via automatic differentiation, J. Chem. Theory Comput. 21, 4742 (2025). We also follow their heat-capacity pipeline.
- RASPA2: Structures of the four giant MOFs (MOF-177, MOF-210, MIL-100(Cr), and MIL-101(Cr)), taken from the CIF library shipped with RASPA2. Experimental heat capacities for MOF-177 and MIL-101(Cr) were transcribed from the primary calorimetry papers, Kloutse et al. (2015) and Liu et al. (2017).
- MACE-MP-0 and PET-MAD: The foundation models used throughout, MACE-MP-0 "medium" and PET-MAD v1.5.0 ("s" and "xs" variants). The archive ships instructions to rebuild the exact checkpoints we used, but not the weights themselves.