# Differentiable Thermodynamic Phase-Equilibria for Machine Learning

arXiv: https://arxiv.org/abs/2603.11249 · HTML: https://mlsanity.com/paper/2603.11249/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 60 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Numerical Coordinate Regression with Convolutional Neural Networks](https://mlsanity.com/paper/1801.07372/) (2018)
- [A smile is all you need: Predicting limiting activity coefficients from SMILES with natural language processing](https://mlsanity.com/paper/2206.07048/) (2022)
- [Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction](https://mlsanity.com/paper/2306.07937/) (2023)
- [HANNA: Hard-constraint Neural Network for Consistent Activity Coefficient Prediction](https://mlsanity.com/paper/2407.18011/) (2024)
- [Thermodynamics-Consistent Graph Neural Networks](https://mlsanity.com/paper/2407.18372/) (2024)
- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [Global Optimization via Softmin Energy Minimization](https://mlsanity.com/paper/2509.17815/) (2025)

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

- [Blind Thermodynamic Ontology Discovery from Anonymous Experiments](https://mlsanity.com/paper/2609.23387/) (2026)

## Abstract (arXiv)

Accurate prediction of phase equilibria remains a central challenge in chemical engineering. Physics-consistent machine learning methods that incorporate thermodynamic structure into neural networks have recently shown strong performance for activity-coefficient modeling. However, extending such approaches to equilibrium data arising from an extremum principle, such as liquid-liquid equilibria, remains difficult. Here we present DISCOMAX, a differentiable algorithm for phase-equilibrium calculation that guarantees thermodynamic consistency at both training and inference, only subject to a user-specified discretization. The method combines discrete enumeration of feasible phase states with masked softmax aggregation in the backward pass, with the propagation of the true equilibrium state in the forward pass, using a straight-through gradient estimator to enable physics-consistent end-to-end learning of neural glsgE-models. We show that this approach bears analogy to statistical thermodynamics, and we evaluate it on binary liquid-liquid equilibrium data where it outperforms existing surrogate-based methods, while offering a general framework for learning from different kinds of equilibrium data.