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Pushing the limits of unconstrained machine-learned interatomic potentials

Filippo Bigi, Paolo Pegolo, Arslan Mazitov, Michele Ceriotti

TL;DR

The paper investigates unconstrained machine-learned interatomic potentials (MLIPs) that relax exact physical symmetries, showing that with large, diverse training data they can match or surpass constrained models in accuracy and speed. It introduces the PET architecture, a transformer-based GNN that scales to hundreds of millions of parameters and supports direct-force heads and adaptive cutoffs, while enabling inference-time symmetry restoration. The authors demonstrate state-of-the-art performance on large materials benchmarks (matbench-discovery) and strong results on molecular benchmarks (SPICE) after pretraining on non-conservative data and fine-tuning. They provide practical guidance for using unconstrained models in geometry optimization and lattice dynamics, including strategies like rotational averaging and careful handling of symmetry-related observables. Overall, unconstrained PET models offer a viable, efficient path to general-purpose, high-accuracy MLIPs with scalable training and flexible downstream use cases.

Abstract

Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to fulfill a number of physical laws exactly, from geometric symmetries to energy conservation. Evidence is mounting that relaxing some of these constraints can be beneficial to the efficiency and (somewhat surprisingly) accuracy of MLIPs, even though care should be taken to avoid qualitative failures associated with the breaking of physical symmetries. Given the recent trend of \emph{scaling up} models to larger numbers of parameters and training samples, a very important question is how unconstrained MLIPs behave in this limit. Here we investigate this issue, showing that -- when trained on large datasets -- unconstrained models can be superior in accuracy and speed when compared to physically constrained models. We assess these models both in terms of benchmark accuracy and in terms of usability in practical scenarios, focusing on static simulation workflows such as geometry optimization and lattice dynamics. We conclude that accurate unconstrained models can be applied with confidence, especially since simple inference-time modifications can be used to recover observables that are consistent with the relevant physical symmetries.

Pushing the limits of unconstrained machine-learned interatomic potentials

TL;DR

The paper investigates unconstrained machine-learned interatomic potentials (MLIPs) that relax exact physical symmetries, showing that with large, diverse training data they can match or surpass constrained models in accuracy and speed. It introduces the PET architecture, a transformer-based GNN that scales to hundreds of millions of parameters and supports direct-force heads and adaptive cutoffs, while enabling inference-time symmetry restoration. The authors demonstrate state-of-the-art performance on large materials benchmarks (matbench-discovery) and strong results on molecular benchmarks (SPICE) after pretraining on non-conservative data and fine-tuning. They provide practical guidance for using unconstrained models in geometry optimization and lattice dynamics, including strategies like rotational averaging and careful handling of symmetry-related observables. Overall, unconstrained PET models offer a viable, efficient path to general-purpose, high-accuracy MLIPs with scalable training and flexible downstream use cases.

Abstract

Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to fulfill a number of physical laws exactly, from geometric symmetries to energy conservation. Evidence is mounting that relaxing some of these constraints can be beneficial to the efficiency and (somewhat surprisingly) accuracy of MLIPs, even though care should be taken to avoid qualitative failures associated with the breaking of physical symmetries. Given the recent trend of \emph{scaling up} models to larger numbers of parameters and training samples, a very important question is how unconstrained MLIPs behave in this limit. Here we investigate this issue, showing that -- when trained on large datasets -- unconstrained models can be superior in accuracy and speed when compared to physically constrained models. We assess these models both in terms of benchmark accuracy and in terms of usability in practical scenarios, focusing on static simulation workflows such as geometry optimization and lattice dynamics. We conclude that accurate unconstrained models can be applied with confidence, especially since simple inference-time modifications can be used to recover observables that are consistent with the relevant physical symmetries.
Paper Structure (44 sections, 5 equations, 8 figures, 12 tables)

This paper contains 44 sections, 5 equations, 8 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Background and related work
  3. Interatomic potentials and their properties
  4. E(3)-invariance.
  5. Permutational invariance.
  6. Locality.
  7. Machine-learned interatomic potentials
  8. Interatomic potentials and forces
  9. Applications and benchmarks
  10. Theory and methods
  11. What determines whether a symmetry is learnable?
  12. Translations.
  13. Permutations.
  14. Rotations.
  15. Inversions.
  16. ...and 29 more sections

Figures (8)

  • Figure 1: Illustration of the proposed architecture. $a_i$ and $a_{ij}$ are the chemical elements of a center atom and a neighbor atom, respectively. $E_i$ represents an atomic energy; all atomic energies are summed to obtain the total energy. *Attention weights are scaled to ensure smoothness as described in Ref. pozd-ceri23nips.
  • Figure 2: Geometry optimization and phonon calculations with PET-OAM. (a,b) Deviation of unit-cell lengths as a function of the maximum generalized force (force and stress component, as returned by ASE's "FrechetCellFilter") for BCC (a) and HCP (b) starting configurations. (c--e) Phonon bands of titanium starting from BCC, using conservative PET after constrained (c) and unconstrained (d) relaxation, and non-conservative PET after unconstrained relaxation (e). (g--i) Corresponding calculations starting from HCP. (f,j) Vibrational density of states for the two sets of calculations.
  • Figure 3: Accuracy-speed Pareto front for models trained on the SPICE dataset, at varying structure sizes. The energy error on the x-axis is the average of all subset-specific errors. Model sizes for the six benchmarked models are shown in the middle panel. More details are available in App. \ref{['app:spice']}.
  • Figure A1: Histogram of the number of neighbors selected by the adaptive cutoff algorithm with different target $\bar{n}$, and compared with that for a fixed cutoff of 6Å. The dataset is a collection of 2700 structures randomly selected from the highly diverse MAD dataset mad.
  • Figure A2: Pareto plot of accuracy (force MAE on a hold-out test set) and computational cost (measured from ASE ase-paper) for a series of PET models trained on the OMat24 dataset. The maximum system size that can be reached before hitting an out-of-memory error on the hardware we used (a single NVIDIA H100 GPU with 92 GB of memory) is visualized as the color and size of the data points.
  • ...and 3 more figures