Thermodynamics-Informed Learning Captures Hierarchical Hydrogen-Bond Networks in Deep Eutectic Solvents

Accurate prediction of hydrogen sorption in fine-grained geological materials is essential for evaluating underground hydrogen storage capacity, assessing caprock integrity, and characterizing hydrogen migration in subsurface energy systems. Classical isotherm models perform well at the individual-sample level but fail when generalized across heterogeneous populations, with the coefficient of determination collapsing from 0.80-0.90 for single-sample fits to 0.09-0.38 for aggregated multi-sample datasets. We present a multi-scale physics-informed neural network framework that addresses this limitation by embedding classical adsorption theory and thermodynamic constraints directly into the learning process. The framework utilizes 1,987 hydrogen sorption isotherm measurements across clays, shales, coals, supplemented by 224 characteristic uptake measurements. A seven-category physics-informed feature engineering scheme generates 62 thermodynamically meaningful descriptors from raw material characterization data. The loss function enforces saturation limits, a monotonic pressure response, and Van't Hoff temperature dependence via penalty weighting, while a three-phase curriculum-based training strategy ensures stable integration of competing physical constraints. An architecture-diverse ensemble of ten members provides calibrated uncertainty quantification, with post-hoc temperature scaling achieving target prediction interval coverage. The optimized PINN achieves R2 = 0.9544, RMSE = 0.0484 mmol/g, and MAE = 0.0231 mmol/g on the held-out test set, with 98.6% monotonicity satisfaction and zero non-physical negative predictions. Physics-informed regularization yields a 10-15% cross-lithology generalization advantage over a well-tuned random forest under leave-one-lithology-out validation, confirming that thermodynamic constraints transfer meaningfully across geological boundaries.

Molecular solubility directly affects key aspects of molecular development such as reaction feasibility, formulation performance, separation efficiency, and solvent selection. However, experimental measurement across solutes, solvents, and temperatures remains costly and sparsely sampled. Existing computational models often rely on fixed-solvent assumptions, deterministic formulations, or simplified representations of solute-solvent interactions, limiting their ability to capture complex molecular interactions, continuous temperature effects, and experimental uncertainty. Here, we introduce EnSol, an environment-aware probabilistic framework for molecular solubility prediction. EnSol represents the solute and solvent as molecular graphs and learns separate representations for each before bringing them together through cross-attention to capture solute-solvent interactions. Temperature is incorporated directly into the solvent environment through feature-wise modulation, and a mixture density network predicts full solubility distributions to capture both temperature-dependent behavior and experimental uncertainty. On the independent SolProp and Leeds benchmark datasets, EnSol achieved Spearman correlations of 0.876 and 0.601, respectively, outperforming state-of-the-art solubility prediction models across both benchmarks. Beyond computational benchmarking, experimental validation across chemically diverse solute-solvent pairs showed that EnSol maintained strong predictive performance and supported reliable solvent ranking, achieving a Spearman correlation of 0.715. These results show that EnSol can support reliable solubility prediction and solvent selection across diverse chemical systems while accounting for predictive uncertainty.

High-fidelity solubility prediction is fundamental to pharmaceutical development and environmental partitioning, where accurate modeling must couple molecular structure with thermodynamic behavior across diverse chemical environments. However, recent advancements have been dominated by deep learning architectures that often sacrifice physical interpretability for predictive power. We challenge this trend by showing that state-of-the-art performance does not require such non-transparent architectures. To address this, we introduce DISSOLVR, a transparent framework for molecular solubility prediction. In addition, we perform a comprehensive literature review and a benchmarking study against various methods. We show that DISSOLVR approaches the aleatoric limit of experimental uncertainty and achieves OOD generalization through structural invariance, derived by mapping molecules to physically-grounded descriptors. Then, we present an LLM-assisted post-hoc explanation pipeline that bridges the gap between symbolic model artifacts and chemically grounded narratives. Finally, a comparative benchmark of a survey involving 22 expert chemists reveals that expert evaluators provide deep insights.