# Machine Learning Force Fields

arXiv: https://arxiv.org/abs/2010.07067 · HTML: https://mlsanity.com/paper/2010.07067/

## Key facts

- Cited by 207 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2020.

## Built on by (most cited first, 30 of 207)

- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [SELFIES and the future of molecular string representations](https://mlsanity.com/paper/2204.00056/) (2022)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
- [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (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)
- [So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems](https://mlsanity.com/paper/2205.14276/) (2022)
- [Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths](https://mlsanity.com/paper/2207.02149/) (2022)
- [Transition1x -- a Dataset for Building Generalizable Reactive Machine Learning Potentials](https://mlsanity.com/paper/2207.12858/) (2022)
- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [Toward Explainable AI for Regression Models](https://mlsanity.com/paper/2112.11407/) (2021)
- [Cartesian atomic cluster expansion for machine learning interatomic potentials](https://mlsanity.com/paper/2402.07472/) (2024)
- [Diffeomorphic Counterfactuals with Generative Models](https://mlsanity.com/paper/2206.05075/) (2022)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [SchNetPack 2.0: A neural network toolbox for atomistic machine learning](https://mlsanity.com/paper/2212.05517/) (2022)
- [Latent Ewald summation for machine learning of long-range interactions](https://mlsanity.com/paper/2408.15165/) (2024)
- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids](https://mlsanity.com/paper/2112.00652/) (2021)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [The dark side of the forces: assessing non-conservative force models for atomistic machine learning](https://mlsanity.com/paper/2412.11569/) (2024)
- [Simulate Time-integrated Coarse-grained Molecular Dynamics with Multi-Scale Graph Networks](https://mlsanity.com/paper/2204.10348/) (2022)
- [PET-MAD, a lightweight universal interatomic potential for advanced materials modeling](https://mlsanity.com/paper/2503.14118/) (2025)
- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [PILOT: Equivariant diffusion for pocket conditioned de novo ligand generation with multi-objective guidance via importance sampling](https://mlsanity.com/paper/2405.14925/) (2024)
- [Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials](https://mlsanity.com/paper/2312.01416/) (2023)
- [DPA-1: Pretraining of Attention-based Deep Potential Model for Molecular Simulation](https://mlsanity.com/paper/2208.08236/) (2022)

## Abstract (arXiv)

In recent years, the use of Machine Learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.