# Physics- and data-driven Active Learning of neural network representations for free energy functions of materials from statistical mechanics

arXiv: https://arxiv.org/abs/2503.07619 · HTML: https://mlsanity.com/paper/2503.07619/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 25 Feb 2025.

## Builds on (most cited first, 4 of 4)

- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Gaussian Switch Sampling: A Second Order Approach to Active Learning](https://mlsanity.com/paper/2302.12018/) (2023)
- [Scale bridging materials physics: Active learning workflows and integrable deep neural networks for free energy function representations in alloys](https://mlsanity.com/paper/2002.02305/) (2020)
- [Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order disorder transitions in LixCoO2](https://mlsanity.com/paper/2302.08991/) (2023)

## Abstract (arXiv)

Accurate free energy representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy model by training a neural network on DFT-informed Monte Carlo data. To optimize sampling in the high-dimensional Monte Carlo space, we present an Active Learning framework that integrates space-filling sampling, uncertainty-based sampling, and physics-informed sampling. Additionally, our approach includes methods such as hyperparameter tuning, dynamic sampling, and novelty enforcement. These strategies can be combined to reduce MSE,either globally or in targeted regions of interest,while minimizing the number of required data points. The framework introduced here is broadly applicable to Monte Carlo sampling of a range of materials systems.