DEEP LEARNING HELMHOLTZ ENERGIES FOR THERMODYNAMIC PROPERTY PREDICTION
- 1Chimie ParisTech
- 2Université PSL, CNRS Institute of Chemistry for Life and Health Sciences
- 3CNRS Laboratoire Interdisciplinaire de Physique (LIPhy
Abstract
Based on SAFT equations of state (EoS), we propose a physics informed neural network that learns the residual Helmholtz free energy, yielding pressure, chemical potentials, entropy, and phase equilibria by automatic differentiation. Transport properties are connected through additional relations. The model can be pretrained on synthetic EoS data and fine-tuned with heterogeneous experimental data. The model operates on logarithmic scale and is designed to stabilize learning properties that span several orders of magnitude between phases, state points, and molecules. A differentiable transport model further allows viscosity and self-diffusion data to learn the temperature derivative of the Helmholtz energy during fine-tuning. As a proof of concept, we fine-tune the model to experimental temperature–pressure–density, viscosity, and self-diffusion data for water. Despite using only state point information and transport data for this single, particularly challenging fluid, the model predicts vapor pressure, vaporization enthalpy, density and entropy anomalies, and the critical temperature without direct exposure to these properties during fine-tuning. This demonstrates that jointly learning Helmholtz energies and transport coefficients is viable and beneficial. We argue that such Helmholtz energy centered, data driven deep learning models provide an alternative to the current proliferation of isolated, single property machine learning solutions. Generalization to unseen molecules and a fixed functional mode with optimized molecule representation parameters are also demonstrated.
Related
- Transfer Protocol Matters More Than Source-Task Selection in Low-Data Molecular Property Prediction: An Audit of QM9 Pretraining on Computed Oxidation Potentials and Redox Reaction Energies
- Topology-Guided Multi-Level Graph Learning: A Unified Framework for Molecular Property Prediction
- Beyond conventional sequence-based encoding: a generalized Machine Learning pipeline for oligonucleotide property prediction
- Machine learning-aided design of metallic mechanical metamaterials: fabrication-aware modelling, property prediction, and inverse design
- P2MAT: A machine learning (ML) driven software for Property Prediction of MATerial
BibTeX
@misc{fleck2026deep,
title = {{DEEP LEARNING HELMHOLTZ ENERGIES FOR THERMODYNAMIC PROPERTY PREDICTION}},
author = {Maximilian Fleck and Marcelle B M Spera},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15008626/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008626/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - DEEP LEARNING HELMHOLTZ ENERGIES FOR THERMODYNAMIC PROPERTY PREDICTION
AU - Maximilian Fleck
AU - Marcelle B M Spera
PY - 2026
DA - 2026/09/10
PB - ChemRxiv
DO - 10.26434/chemrxiv.15008626/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008626/v1
AB - Based on SAFT equations of state (EoS), we propose a physics informed neural network that learns the residual Helmholtz free energy, yielding pressure, chemical potentials, entropy, and phase equilibria by automatic differentiation. Transport properties are connected through additional relations. The model can be pretrained on synthetic EoS data and fine-tuned with heterogeneous experimental data. The model operates on logarithmic scale and is designed to stabilize learning properties that span several orders of magnitude between phases, state points, and molecules. A differentiable transport model further allows viscosity and self-diffusion data to learn the temperature derivative of the Helmholtz energy during fine-tuning. As a proof of concept, we fine-tune the model to experimental temperature–pressure–density, viscosity, and self-diffusion data for water. Despite using only state point information and transport data for this single, particularly challenging fluid, the model predicts vapor pressure, vaporization enthalpy, density and entropy anomalies, and the critical temperature without direct exposure to these properties during fine-tuning. This demonstrates that jointly learning Helmholtz energies and transport coefficients is viable and beneficial. We argue that such Helmholtz energy centered, data driven deep learning models provide an alternative to the current proliferation of isolated, single property machine learning solutions. Generalization to unseen molecules and a fixed functional mode with optimized molecule representation parameters are also demonstrated.
ER -