# The dark side of the forces: assessing non-conservative force models for atomistic machine learning

arXiv: https://arxiv.org/abs/2412.11569 · HTML: https://mlsanity.com/paper/2412.11569/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 77 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalysts](https://mlsanity.com/paper/2206.08917/) (2022)
- [SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials](https://mlsanity.com/paper/2209.10702/) (2022)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Orb: A Fast, Scalable Neural Network Potential](https://mlsanity.com/paper/2410.22570/) (2024)
- [Open Materials 2024 (OMat24) Inorganic Materials Dataset and Models](https://mlsanity.com/paper/2410.12771/) (2024)
- [Protein Conformation Generation via Force-Guided SE(3) Diffusion Models](https://mlsanity.com/paper/2403.14088/) (2024)
- [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)
- [Smooth, exact rotational symmetrization for deep learning on point clouds](https://mlsanity.com/paper/2305.19302/) (2023)
- [Revisiting Data Augmentation for Rotational Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/2310.08429/) (2023)
- [Unified theory of atom-centered representations and message-passing machine-learning schemes](https://mlsanity.com/paper/2202.01566/) (2022)
- [Probing the effects of broken symmetries in machine learning](https://mlsanity.com/paper/2406.17747/) (2024)
- [Physical Consistency Bridges Heterogeneous Data in Molecular Multi-Task Learning](https://mlsanity.com/paper/2410.10118/) (2024)

## Built on by (most cited first, 24 of 24)

- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [PET-MAD, a lightweight universal interatomic potential for advanced materials modeling](https://mlsanity.com/paper/2503.14118/) (2025)
- [Towards Fast, Specialized Machine Learning Force Fields: Distilling Foundation Models via Energy Hessians](https://mlsanity.com/paper/2501.09009/) (2025)
- [FlashMD: long-stride, universal prediction of molecular dynamics](https://mlsanity.com/paper/2505.19350/) (2025)
- [Pushing the limits of unconstrained machine-learned interatomic potentials](https://mlsanity.com/paper/2601.16195/) (2026)
- [EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformers](https://mlsanity.com/paper/2604.09130/) (2026)
- [How simple can you go? An off-the-shelf transformer approach to molecular dynamics](https://mlsanity.com/paper/2503.01431/) (2025)
- [MOFSimBench: Evaluating Universal Machine Learning Interatomic Potentials In Metal--Organic Framework Molecular Modeling](https://mlsanity.com/paper/2507.11806/) (2025)
- [Learning from the electronic structure of molecules across the periodic table](https://mlsanity.com/paper/2510.00224/) (2025)
- [Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics](https://mlsanity.com/paper/2601.22123/) (2026)
- [MatRIS: Toward Reliable and Efficient Pretrained Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2603.02002/) (2026)
- [Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Space](https://mlsanity.com/paper/2509.14961/) (2025)
- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)
- [Scaling Laws and Symmetry, Evidence from Neural Force Fields](https://mlsanity.com/paper/2510.09768/) (2025)
- [ADAPT: Lightweight, Long-Range Machine Learning Force Fields Without Graphs](https://mlsanity.com/paper/2509.24115/) (2025)
- [AceFF: A State-of-the-Art Machine Learning Potential for Small Molecules](https://mlsanity.com/paper/2601.00581/) (2026)
- [From Evaluation to Design: Using Potential Energy Surface Smoothness Metrics to Guide Machine Learning Interatomic Potential Architectures](https://mlsanity.com/paper/2602.04861/) (2026)
- [Faster Molecular Dynamics with Neural Network Potentials via Distilled Multiple Time-Stepping and Non-Conservative Forces](https://mlsanity.com/paper/2602.14975/) (2026)
- [How unconstrained machine-learning models learn physical symmetries](https://mlsanity.com/paper/2603.24638/) (2026)
- [Speculative Sampling For Faster Molecular Dynamics](https://mlsanity.com/paper/2606.02455/) (2026)
- [Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations](https://mlsanity.com/paper/2607.29158/) (2026)
- [Truncated automatic sparse differentiation for machine learning interatomic potentials](https://mlsanity.com/paper/2609.20510/) (2026)
- [On the Theoretical Limits of Learning Unconstrained Interatomic Potentials](https://mlsanity.com/paper/2610.15078/) (2026)

## Abstract (arXiv)

The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, has revolutionized the fields of computational chemistry and materials discovery. In this domain, rigorous enforcement of symmetry and conservation laws has traditionally been considered essential. For this reason, interatomic forces are usually computed as the derivatives of the potential energy, ensuring energy conservation. Several recent works have questioned this physically constrained approach, suggesting that directly predicting the forces yields a better trade-off between accuracy and computational efficiency, and that energy conservation can be learned during training. This work investigates the applicability of such non-conservative models in microscopic simulations. We identify and demonstrate several fundamental issues, from ill-defined convergence of geometry optimization to instability in various types of molecular dynamics. Given the difficulty in monitoring and correcting the lack of energy conservation, direct forces should be used with great care. We show that the best approach to exploit the acceleration they afford is to use them in conjunction with conservative forces. A model can be pre-trained efficiently on direct forces, then fine-tuned using backpropagation. At evaluation time, both force types can be used together to avoid unphysical effects while still benefitting almost entirely from the computational efficiency of direct forces.