# Learning Collective Variables with Synthetic Data Augmentation through Physics-Inspired Geodesic Interpolation

arXiv: https://arxiv.org/abs/2402.01542 · HTML: https://mlsanity.com/paper/2402.01542/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 53 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 5 of 5)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Automated design of collective variables using supervised machine learning](https://mlsanity.com/paper/1802.10510/) (2018)
- [Multitask machine learning of collective variables for enhanced sampling of rare events](https://mlsanity.com/paper/2012.03909/) (2020)
- [Differentiable Simulations for Enhanced Sampling of Rare Events](https://mlsanity.com/paper/2301.03480/) (2023)
- [Data-driven path collective variables](https://mlsanity.com/paper/2312.13868/) (2023)

## Built on by (most cited first, 6 of 6)

- [Scaling Autoregressive Models for Lattice Thermodynamics](https://mlsanity.com/paper/2603.14695/) (2026)
- [Transferable Learning of Reaction Pathways from Geometric Priors](https://mlsanity.com/paper/2504.15370/) (2025)
- [Riemannian Denoising Model for Molecular Structure Optimization with Chemical Accuracy](https://mlsanity.com/paper/2411.19769/) (2024)
- [Learning Collective Variables from BioEmu with Time-Lagged Generation](https://mlsanity.com/paper/2507.07390/) (2025)
- [Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamics](https://mlsanity.com/paper/2604.25244/) (2026)
- [A Supervised Machine Learning Framework for Multipactor Breakdown Prediction in High-Power Radio Frequency Devices and Accelerator Components: A Case Study in Planar Geometry](https://mlsanity.com/paper/2507.17881/) (2025)

## Abstract (arXiv)

In molecular dynamics simulations, rare events, such as protein folding, are typically studied using enhanced sampling techniques, most of which are based on the definition of a collective variable (CV) along which acceleration occurs. Obtaining an expressive CV is crucial, but often hindered by the lack of information about the particular event, e.g., the transition from unfolded to folded conformation. We propose a simulation-free data augmentation strategy using physics-inspired metrics to generate geodesic interpolations resembling protein folding transitions, thereby improving sampling efficiency without true transition state samples. This new data can be used to improve the accuracy of classifier-based methods. Alternatively, a regression-based learning scheme for CV models can be adopted by leveraging the interpolation progress parameter.