# Accurate machine learning force fields via experimental and simulation data fusion

arXiv: https://arxiv.org/abs/2308.09142 · HTML: https://mlsanity.com/paper/2308.09142/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 88 references that are in the map.
- First posted on arXiv 17 Aug 2023.

## Builds on (most cited first, 16 of 16)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [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)
- [Less is more: sampling chemical space with active learning](https://mlsanity.com/paper/1801.09319/) (2018)
- [GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasets](https://mlsanity.com/paper/2204.02782/) (2022)
- [TorchMD: A deep learning framework for molecular simulations](https://mlsanity.com/paper/2012.12106/) (2020)
- [Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation](https://mlsanity.com/paper/1810.11890/) (2018)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Learning neural network potentials from experimental data via Differentiable Trajectory Reweighting](https://mlsanity.com/paper/2106.01138/) (2021)
- [Differentiable Molecular Simulations for Control and Learning](https://mlsanity.com/paper/2003.00868/) (2020)
- [Fast Uncertainty Estimates in Deep Learning Interatomic Potentials](https://mlsanity.com/paper/2211.09866/) (2022)
- [Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls](https://mlsanity.com/paper/2212.07959/) (2022)
- [Learning Pair Potentials using Differentiable Simulations](https://mlsanity.com/paper/2209.07679/) (2022)
- [Top-down machine learning of coarse-grained protein force-fields](https://mlsanity.com/paper/2306.11375/) (2023)

## Built on by (most cited first, 12 of 12)

- [chemtrain: Learning Deep Potential Models via Automatic Differentiation and Statistical Physics](https://mlsanity.com/paper/2408.15852/) (2024)
- [Predicting solvation free energies with an implicit solvent machine learning potential](https://mlsanity.com/paper/2406.00183/) (2024)
- [Stability-Aware Training of Machine Learning Force Fields with Differentiable Boltzmann Estimators](https://mlsanity.com/paper/2402.13984/) (2024)
- [Artificial Intelligence and Generative Models for Materials Discovery -- A Review](https://mlsanity.com/paper/2508.03278/) (2025)
- [Learning Non-Local Molecular Interactions via Equivariant Local Representations and Charge Equilibration](https://mlsanity.com/paper/2501.19179/) (2025)
- [Enhancing Machine Learning Potentials through Transfer Learning across Chemical Elements](https://mlsanity.com/paper/2502.13522/) (2025)
- [Morphology-Aware Peptide Discovery via Masked Conditional Generative Modeling](https://mlsanity.com/paper/2509.02060/) (2025)
- [Building Trustworthy AI for Materials Discovery: From Autonomous Laboratories to Z-scores](https://mlsanity.com/paper/2512.01080/) (2025)
- [Self-Optimizing Machine Learning Potential Assisted Automated Workflow for Highly Efficient Complex Systems Material Design](https://mlsanity.com/paper/2505.08159/) (2025)
- [Refining Machine Learning Potentials through Thermodynamic Theory of Phase Transitions](https://mlsanity.com/paper/2512.03974/) (2025)
- [WISCA: A Consensus-Based Approach to Harmonizing Interpretability in Tabular Datasets](https://mlsanity.com/paper/2506.06455/) (2025)
- [Iterative Pretraining Framework for Interatomic Potentials](https://mlsanity.com/paper/2507.20118/) (2025)

## Abstract (arXiv)

Machine Learning (ML)-based force fields are attracting ever-increasing interest due to their capacity to span spatiotemporal scales of classical interatomic potentials at quantum-level accuracy. They can be trained based on high-fidelity simulations or experiments, the former being the common case. However, both approaches are impaired by scarce and erroneous data resulting in models that either do not agree with well-known experimental observations or are under-constrained and only reproduce some properties. Here we leverage both Density Functional Theory (DFT) calculations and experimentally measured mechanical properties and lattice parameters to train an ML potential of titanium. We demonstrate that the fused data learning strategy can concurrently satisfy all target objectives, thus resulting in a molecular model of higher accuracy compared to the models trained with a single data source. The inaccuracies of DFT functionals at target experimental properties were corrected, while the investigated off-target properties remained largely unperturbed. Our approach is applicable to any material and can serve as a general strategy to obtain highly accurate ML potentials.