# Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Science

arXiv: https://arxiv.org/abs/2305.14247 · HTML: https://mlsanity.com/paper/2305.14247/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 93 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 30 of 34)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Scaling description of generalization with number of parameters in deep learning](https://mlsanity.com/paper/1901.01608/) (2019)
- [Less is more: sampling chemical space with active learning](https://mlsanity.com/paper/1801.09319/) (2018)
- [Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspective](https://mlsanity.com/paper/1906.11081/) (2019)
- [Simple GNN Regularisation for 3D Molecular Property Prediction & Beyond](https://mlsanity.com/paper/2106.07971/) (2021)
- [Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size](https://mlsanity.com/paper/2304.10061/) (2023)
- [Equivariant Graph Attention Networks for Molecular Property Prediction](https://mlsanity.com/paper/2202.09891/) (2022)
- [TeaNet: universal neural network interatomic potential inspired by iterative electronic relaxations](https://mlsanity.com/paper/1912.01398/) (2019)
- [Unified theory of atom-centered representations and message-passing machine-learning schemes](https://mlsanity.com/paper/2202.01566/) (2022)

## Built on by (most cited first, 25 of 25)

- [TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentials](https://mlsanity.com/paper/2306.06482/) (2023)
- [The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domains](https://mlsanity.com/paper/2410.24169/) (2024)
- [From Molecules to Materials: Pre-training Large Generalizable Models for Atomic Property Prediction](https://mlsanity.com/paper/2310.16802/) (2023)
- [Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Products](https://mlsanity.com/paper/2401.10216/) (2024)
- [Impacts of floating-point non-associativity on reproducibility for HPC and deep learning applications](https://mlsanity.com/paper/2408.05148/) (2024)
- [Force-Free Molecular Dynamics Through Autoregressive Equivariant Networks](https://mlsanity.com/paper/2503.23794/) (2025)
- [Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systems](https://mlsanity.com/paper/2502.19227/) (2025)
- [Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing](https://mlsanity.com/paper/2405.14253/) (2024)
- [On the Completeness of Invariant Geometric Deep Learning Models](https://mlsanity.com/paper/2402.04836/) (2024)
- [MACE-POLAR-1: A Polarisable Electrostatic Foundation Model for Molecular Chemistry](https://mlsanity.com/paper/2602.19411/) (2026)
- [Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Space](https://mlsanity.com/paper/2509.14961/) (2025)
- [On the design space between molecular mechanics and machine learning force fields](https://mlsanity.com/paper/2409.01931/) (2024)
- [Equivariant Matrix Function Neural Networks](https://mlsanity.com/paper/2310.10434/) (2023)
- [Accurate Crystal Structure Prediction of New 2D Hybrid Organic Inorganic Perovskites](https://mlsanity.com/paper/2403.06955/) (2024)
- [BOOM: Benchmarking Out-Of-distribution Molecular Property Predictions of Machine Learning Models](https://mlsanity.com/paper/2505.01912/) (2025)
- [A Cartesian-3j Framework for Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2512.16882/) (2025)
- [Efficient and Accurate Spatial Mixing of Machine Learned Interatomic Potentials for Materials Science](https://mlsanity.com/paper/2502.19081/) (2025)
- [Optimal Invariant Bases for Atomistic Machine Learning](https://mlsanity.com/paper/2503.23515/) (2025)
- [Optimizing Data Distribution and Kernel Performance for Efficient Training of Chemistry Foundation Models: A Case Study with MACE](https://mlsanity.com/paper/2504.10700/) (2025)
- [Machine-Learned Atomic Cluster Expansion Potentials for Fast and Quantum-Accurate Thermal Simulations of Wurtzite AlN](https://mlsanity.com/paper/2311.11990/) (2023)
- [Global Universal Scaling and Ultra-Small Parameterization in Machine Learning Interatomic Potentials with Super-Linearity](https://mlsanity.com/paper/2502.07293/) (2025)
- [On-the-Fly Fine-Tuning of Foundational Neural Network Potentials: A Bayesian Neural Network Approach](https://mlsanity.com/paper/2507.13805/) (2025)
- [Neutron and X-ray Diffraction Reveal the Limits of Long-Range Machine Learning Potentials for Medium-Range Order in Silica Glass](https://mlsanity.com/paper/2604.21222/) (2026)
- [Triply-Scalable Equivariant Gaussian Process Modeling](https://mlsanity.com/paper/2609.21085/) (2026)
- [SoLiD26: A First Principles Solid-Liquid Interface Dataset for Machine-learned Interatomic Potentials](https://mlsanity.com/paper/2609.28013/) (2026)

## Abstract (arXiv)

The MACE architecture represents the state of the art in the field of machine learning force fields for a variety of in-domain, extrapolation and low-data regime tasks. In this paper, we further evaluate MACE by fitting models for published benchmark datasets. We show that MACE generally outperforms alternatives for a wide range of systems from amorphous carbon, universal materials modelling, and general small molecule organic chemistry to large molecules and liquid water. We demonstrate the capabilities of the model on tasks ranging from constrained geometry optimisation to molecular dynamics simulations and find excellent performance across all tested domains. We show that MACE is very data efficient, and can reproduce experimental molecular vibrational spectra when trained on as few as 50 randomly selected reference configurations. We further demonstrate that the strictly local atom-centered model is sufficient for such tasks even in the case of large molecules and weakly interacting molecular assemblies.