# Multi-Label Phase Diagram Prediction in Complex Alloys via Physics-Informed Graph Attention Networks

arXiv: https://arxiv.org/abs/2604.16468 · HTML: https://mlsanity.com/paper/2604.16468/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Physics-consistent machine learning: output projection onto physical manifolds](https://mlsanity.com/paper/2502.15755/) (2025)
- [aLLoyM: A large language model for alloy phase diagram prediction](https://mlsanity.com/paper/2507.22558/) (2025)

## Abstract (arXiv)

Accurate phase equilibria are foundational to alloy design because they encode the underlying thermodynamics governing stability, transformations, and processing windows. However, while the CALculation of Phase Diagrams (CALPHAD) provides a rigorous thermodynamic framework, exploring multicomponent composition-temperature space remains computationally expensive and is typically limited to sparse section. To enable rapid phase mapping and alloy screening, we propose a physics-informed graph attention network (GAT) that learns element-aware representations and couples them with thermodynamic constraints for multi-label phase-set prediction in the Ag-Bi-Cu-Sn alloy system. Using about 25,000 equilibrium states generated with pycalphad, each composition-temperature point is represented as a four-node element graph with atomic fractions and elemental descriptors as node features. The model combines graph attention, global pooling, and a multilayer perceptron to predict nine relevant phases. To improve physical consistency, we incorporate thermodynamic constraints, applied as training penalties or as an inference-time projection. Across six binary and three ternary subsystems, the baseline model achieves a macro-F1 score of 0.951 and 93.98% exact-set match, while physics-informed decoding improves robustness and raises exact-set accuracy to about 96% on dense in-domain grids. The surrogate also generalizes to an unseen ternary section with 99.32% exact-set accuracy and to a quaternary section at 700 degC with 91.78% accuracy. These results demonstrate that attention-based graph learning coupled with thermodynamic constraint enforcement provides an effective and physically consistent surrogate for high-resolution phase mapping and extrapolative alloy screening.