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

Yanpeng Ye; Chaoran Duan; Mian Xu; S. Mani Sarathy

cs.LGNov 4, 2026

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

Authors: Yanpeng Ye, Chaoran Duan, Mian Xu, S. Mani Sarathy

Organizations: Clean Energy Research Platform, Physical Science and Engineering Division (PSE), King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia · Key Laboratory of the Three Gorges Reservoir Region’s Eco-environments, Ministry of Education, Institute of Environment and Ecology, Chongqing University, Chongqing 400045, China

Abstract

Deep eutectic solvents (DESs) offer a tunable platform for lignocellulose refining, but their solvation behavior depends on multicomponent hydrogen-bond networks rather than individual constituent properties. We develop TiNN, a thermodynamics-informed neural network that hierarchically represents HBA-HBD association and solute accommodation through a learned free-energy pathway. Trained on 938 records, TiNN achieves a test-set $R^2$ of 0.917 and generalizes to new HBA-HBD combinations and sparse conditions. Ablation identifies solute-specific stabilization as the largest contributor to prediction accuracy, while the importance of hydrogen-bond compatibility depends on the dissolution mechanism. Experimental measurements of glucose, xylan, and Kraft lignin in acidic, basic, and neutral DESs show that TiNN reduces the geometric mean solubility error from more than 23-fold with COSMO-RS to approximately 1.5-fold. Without training on fractionation data, TiNN also distinguishes DES formulations with high and low lignin and hemicellulose removal from corn stover. These results support chemically grounded solvent screening for lignocellulose fractionation.

Figures & tables

Figure 1: Statistical overview of the DES solubility dataset. Distribution of $\log S$ values for (a) all DES–solute systems, (b) carbohydrates, (c) lignin-derived compounds, and (d) gases. The dashed red lines indicate the mean values.

Figure 2: Molecular representation and predictive performance of TiNN. (a) Representation strategies for DES–solute systems. Left: direct concatenation of independently encoded HBA, HBD, and solute embeddings. Right: TiNN first combines the HBA and HBD into a DES representation, incorporating composition and internal hydrogen-bond compatibility, and then integrates the solute through DES–solute hydrogen-bond compatibility. (b–d) Parity plots on the carbohydrate subset for (b) MLP with concatenated HBA, HBD, and solute descriptors, (c) TiNN with concatenated input, and (d) TiNN with the hierarchical three-molecule representation. (e) Training- and test-set predictions of the full TiNN model; the reported test-set metrics are calculated on held-out samples.

Group	Model	MAE	RMSE	$R^{2}$	Spearman
Hierarchical TiNN variants	EGNN-TiNN	0.126	0.242	0.917	0.956
	PaiNN-TiNN	0.123	0.253	0.909	0.954
	DimeNet++-TiNN	0.163	0.665	0.562	0.886
EGNN representation + conventional heads	EGNN-MLP	0.170	0.286	0.884	0.913
EGNN representation + conventional heads	EGNN-XGBoost	0.145	0.493	0.656	0.935
Descriptor and graph baselines	MLP	0.232	0.595	0.498	0.878

Table 1: Comparison of TiNN with alternative models for DES–solute solubility prediction. The models test the effects of 3D molecular encoding, thermodynamics-informed prediction, and descriptor-based representations.

Variant	MAE	RMSE	$R^{2}$	Spearman	$\Delta R^{2}$
Full TiNN	0.126	0.242	0.917	0.956	–
w/o solute-specific free-energy term	0.183	0.417	0.754	0.924	$-0.163$
w/o residual branch	0.173	0.361	0.815	0.937	$-0.102$
w/o temperature branch	0.149	0.284	0.886	0.941	$-0.031$
w/o thermodynamic consistency	0.151	0.280	0.889	0.941	$-0.028$
3D encoder $\rightarrow$ 2D descriptors	0.155	0.273	0.895	0.935	$-0.022$

Table 2: Ablation of TiNN components on the test set. Each variant removes or replaces one component of the full model.

\Delta R^{2}

is relative to the full TiNN.

Figure 3: Condition-dependent response and compositional generalization of TiNN. (a, b) MAE of TiNN, CatBoost, and MLP across HBD:HBA ratio bins (a) and temperature bins (b); gray bars indicate the number of test samples in each bin. (c, d) Temperature-dependent SO 2 solubility in TBAB:Gly and TBAB:EG predicted by TiNN (c) and MLP (d); dash-dotted lines show the experimental trends and gray dashed lines show the predicted trends. (e, f) Out-of-fold parity plots for TiNN (e) and MLP (f) under leave-one-HBA–HBD-pair-out cross-validation. Each of the 81 HBA–HBD combinations was held out once, with all associated records excluded from training. Color indicates point density.

Figure 4: Hydrogen-bond compatibility and experimental validation of TiNN. (a) Ablation of the $H^{\mathrm{rel}}$ input under three perturbations; bracket labels give $R^{2}(\text{Full})-R^{2}(\text{variant})$ and error bars indicate one standard deviation over three splits. (b–g) Distributions of $H_{\text{DES--solute}}^{\mathrm{rel}}$ (b, d, f) and $H_{\text{HBA--HBD}}^{\mathrm{rel}}$ (c, e, g) for carbohydrate, lignin-derived, and gaseous solutes. (h) Measured and predicted solubilities in three DESs at 323.15 K; broken bars mark COSMO-RS predictions of complete miscibility. (i) Normalized TiNN predictions and corn stover fractionation for five DESs selected across the predicted dissolution ranking.

Materials Discovery

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Physics-Informed Neural Networks for Predicting Hydrogen Sorption in Geological Formations: Thermodynamically Constrained Deep Learning Integrating Classical Adsorption Theory

Mohammad Nooraiepour, Mohammad Masoudi, Zezhang Song, Helge Hellevang

Faculty of Mathematics & Natural Sciences, University of Oslo, P.O. Box 1047 Blindern, 0316 Oslo, Norway · SINTEF Industry, Applied Geoscience Department, 7465 Trondheim, Norway · College of Geosciences, China University of Petroleum, Beijing 102249, China

Materials Property Prediction Physics-Informed ML

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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.

Abstract

Materials Discovery

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