Physics-informed deep learning for molecular solubility integrating thermodynamic constraints with neural network architectures

Authors: Masoud Amiri

Abstract

Accurate prediction of aqueous solubility remains a fundamental challenge in drug discovery and molecular design, with traditional machine learning approaches often producing predictions that violate basic thermodynamic principles. Here, we introduce a physics-informed neural network (PINN) framework that explicitly incorporates thermodynamic constraints into the learning process, ensuring physical consistency while improving predictive accuracy. Our approach decomposes solvation free energy into physically interpretable components—cavity formation, electrostatic interactions, van der Waals forces, and hydrogen bonding—and enforces their thermodynamic relationships through custom loss functions. We augment the standard AqSolDB dataset (9982 molecules) with quantum chemistry calculations for 1,500 molecules, providing ground-truth energy decompositions. The physics-informed model achieves RMSE of 0.36 log units on AqSolDB and demonstrates 35% improved performance on scaffold split extrapolation on extrapolation to novel chemical scaffolds compared to purely data-driven approaches. Critically, 96.3% of predictions satisfy stringent thermodynamic consistency (energy conservation error < 2 kJ/mol), compared to only 67.4% for standard neural networks, with major physics violations reduced from 32.6 to 3.7%. This work establishes a general framework for incorporating domain knowledge into molecular property prediction, with immediate applications in drug design, materials discovery, and chemical engineering.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-49635-4.

Introduction

Aqueous solubility determines the bioavailability, formulation, and environmental fate of chemical compounds, making its accurate prediction essential for pharmaceutical development, agrochemical design, and environmental risk assessment^1,2^. Despite decades of research, solubility prediction remains challenging due to the complex interplay of molecular structure, intermolecular forces, and solvent effects. Traditional quantitative structure-property relationship (QSPR) models rely on empirical correlations between molecular descriptors and experimental solubility^3^, while recent deep learning approaches leverage end-to-end learning from molecular representations^4–8^. However, both paradigms share a fundamental they learn purely from data without explicitly encoding the underlying physics governing solvation.

The thermodynamics of molecular solvation is well-established through statistical mechanics and has been validated experimentally for over a century^9–12^. The Gibbs free energy of solvation can be rigorously decomposed into cavity formation (creating space in the solvent), electrostatic interactions (charge-charge and charge-dipole), van der Waals dispersion forces, and hydrogen bonding contributions^13–15^. Each component follows known physical cavity formation scales with molecular surface area, electrostatic energy obeys Coulomb’s law, and hydrogen bonding exhibits characteristic distance and angular dependencies. Despite this wealth of domain knowledge, modern machine learning models treat solubility prediction as a black-box regression problem, potentially learning spurious correlations that violate fundamental physics.

This disconnects between data-driven learning and physical principles manifests in several practical problems. First, models trained on limited chemical space often fail catastrophically when predicting properties of structurally novel molecules, as they extrapolate beyond learned correlations without physical constraints^16,17^. Second, predictions may violate basic thermodynamic relationships, such as energy conservation or the Gibbs-Helmholtz equation, undermining trust in model outputs. Third, purely empirical models require large datasets to achieve acceptable accuracy, limiting their utility in data-scarce domains like novel therapeutic modalities or emerging materials.

Physics-informed neural networks (PINNs) offer a promising solution by embedding domain knowledge directly into the learning objective^18–20^. Originally developed for solving partial differential equations, PINNs have demonstrated remarkable success in fluid dynamics, materials science, and climate modeling^21–24^. The key innovation is augmenting the standard data-fitting loss with physics-based penalty terms that enforce known constraints—differential equations, conservation laws, or boundary conditions. This approach enables training with sparse data, improves extrapolation, and guarantees physical consistency of predictions. Figure 1 illustrates our physics-informed framework, comparing traditional data-driven deep learning with our physics-constrained approach. Traditional models treat prediction as black-box regression, learning spurious correlations that may violate thermodynamics. Our physics-informed model explicitly incorporates domain knowledge through differentiable constraints, ensuring physical consistency while improving accuracy.

Fig. 1Physics-informed neural network framework for molecular solubility prediction. (a) Conceptual comparison shows traditional ML (left) treating prediction as black-box regression versus physics-informed approach (right) incorporating thermodynamic constraints. Traditional models learn spurious correlations and violate physics 32% of the time, while physics-informed learning ensures 96.3% thermodynamic consistency with 14% better accuracy. (b) Thermodynamic decomposition for cavity formation energy + 25 kJ/mol (endothermic solvent displacement), electrostatic energy − 15 kJ/mol (favorable polar interactions), van der Waals − 22 kJ/mol (dispersion forces), hydrogen bonding − 18 kJ/mol from 1 H-bond donor (carboxylic -OH) and 4 acceptors (two carbonyl oxygens, one ester oxygen, one hydroxyl oxygen). Components sum to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ :{\varDelta:G}_{total}:=:-30:kJ/mol