# Neural Network Surrogates for Free Energy Computation of Complex Chemical Systems

arXiv: https://arxiv.org/abs/2510.01396 · HTML: https://mlsanity.com/paper/2510.01396/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 1 Oct 2025.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks](https://mlsanity.com/paper/2007.07442/) (2020)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Hard-constraining Neumann boundary conditions in physics-informed neural networks via Fourier feature embeddings](https://mlsanity.com/paper/2504.01093/) (2025)

## Built on by (most cited first, 1 of 1)

- [Learning Biomolecular Motion: The Physics-Informed Machine Learning Paradigm](https://mlsanity.com/paper/2511.06585/) (2025)

## Abstract (arXiv)

Free energy reconstruction methods such as Gaussian Process Regression (GPR) require Jacobians of the collective variables (CVs), a bottleneck that restricts the use of complex or machine-learned CVs. We introduce a neural network surrogate framework that learns CVs directly from Cartesian coordinates and uses automatic differentiation to provide Jacobians, bypassing analytical forms. On an MgCl2 ion-pairing system, our method achieved high accuracy for both a simple distance CV and a complex coordination-number CV. Moreover, Jacobian errors also followed a near-Gaussian distribution, making them suitable for GPR pipelines. This framework enables gradient-based free energy methods to incorporate complex and machine-learned CVs, broadening the scope of biochemistry and materials simulations.