# Learning neural network potentials from experimental data via Differentiable Trajectory Reweighting

arXiv: https://arxiv.org/abs/2106.01138 · HTML: https://mlsanity.com/paper/2106.01138/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 85 references that are in the map.
- First posted on arXiv 2 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Coarse Graining Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2007.11412/) (2020)
- [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)
- [Differentiable Molecular Simulations for Control and Learning](https://mlsanity.com/paper/2003.00868/) (2020)
- [Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks](https://mlsanity.com/paper/2101.11588/) (2021)
- [Accelerated Simulations of Molecular Systems through Learning of their Effective Dynamics](https://mlsanity.com/paper/2102.08810/) (2021)

## Built on by (most cited first, 26 of 26)

- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Machine Learning Coarse-Grained Potentials of Protein Thermodynamics](https://mlsanity.com/paper/2212.07492/) (2022)
- [Accurate machine learning force fields via experimental and simulation data fusion](https://mlsanity.com/paper/2308.09142/) (2023)
- [chemtrain: Learning Deep Potential Models via Automatic Differentiation and Statistical Physics](https://mlsanity.com/paper/2408.15852/) (2024)
- [Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls](https://mlsanity.com/paper/2212.07959/) (2022)
- [Predicting solvation free energies with an implicit solvent machine learning potential](https://mlsanity.com/paper/2406.00183/) (2024)
- [Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics](https://mlsanity.com/paper/2302.07071/) (2023)
- [Stability-Aware Training of Machine Learning Force Fields with Differentiable Boltzmann Estimators](https://mlsanity.com/paper/2402.13984/) (2024)
- [chemtrain-deploy: A parallel and scalable framework for machine learning potentials in million-atom MD simulations](https://mlsanity.com/paper/2506.04055/) (2025)
- [UniFFBench: Evaluating Universal Machine Learning Force Fields Against Experimental Measurements](https://mlsanity.com/paper/2508.05762/) (2025)
- [Learning Non-Local Molecular Interactions via Equivariant Local Representations and Charge Equilibration](https://mlsanity.com/paper/2501.19179/) (2025)
- [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)
- [On the design space between molecular mechanics and machine learning force fields](https://mlsanity.com/paper/2409.01931/) (2024)
- [Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials](https://mlsanity.com/paper/2510.11148/) (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)
- [Generalization of Long-Range Machine Learning Potentials in Complex Chemical Spaces](https://mlsanity.com/paper/2512.10989/) (2025)
- [JaxSGMC: Modular stochastic gradient MCMC in JAX](https://mlsanity.com/paper/2505.11190/) (2025)
- [Refining Machine Learning Potentials through Thermodynamic Theory of Phase Transitions](https://mlsanity.com/paper/2512.03974/) (2025)
- [ConSolv: Solvent-Conditional Machine Learning Implicit Solvent Potential](https://mlsanity.com/paper/2606.24983/) (2026)
- [Implicit Delta Learning of High Fidelity Neural Network Potentials](https://mlsanity.com/paper/2412.06064/) (2024)
- [Operator Forces For Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2506.19628/) (2025)
- [Coarse-Grained Boltzmann Generators](https://mlsanity.com/paper/2602.10637/) (2026)
- [Transferable Implicit Solvent Machine Learning Potential for Drugs and Proteins Approaching Ab Initio Accuracy](https://mlsanity.com/paper/2607.10887/) (2026)
- [Universal Thermodynamic Interatomic Potentials for Crystalline Materials](https://mlsanity.com/paper/2608.14502/) (2026)

## Abstract (arXiv)

In molecular dynamics (MD), neural network (NN) potentials trained bottom-up on quantum mechanical data have seen tremendous success recently. Top-down approaches that learn NN potentials directly from experimental data have received less attention, typically facing numerical and computational challenges when backpropagating through MD simulations. We present the Differentiable Trajectory Reweighting (DiffTRe) method, which bypasses differentiation through the MD simulation for time-independent observables. Leveraging thermodynamic perturbation theory, we avoid exploding gradients and achieve around 2 orders of magnitude speed-up in gradient computation for top-down learning. We show effectiveness of DiffTRe in learning NN potentials for an atomistic model of diamond and a coarse-grained model of water based on diverse experimental observables including thermodynamic, structural and mechanical properties. Importantly, DiffTRe also generalizes bottom-up structural coarse-graining methods such as iterative Boltzmann inversion to arbitrary potentials. The presented method constitutes an important milestone towards enriching NN potentials with experimental data, particularly when accurate bottom-up data is unavailable.