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Differential Learning for Robust Prediction of Thermal Stability with Application to Energetic Materials
Megan C. Davis, R. Seaton Ullberg, Jeremy N. Schroeder, Andrew H. Salij, Marc J. Cawkwell, Christopher J. Snyder, Ivana Matanovic, Wilton J. M. Kort-Kamp
TL;DR
Laboratory-dependent measurement variability complicates reliable thermal-stability prediction for energetic materials. The paper uses differential learning to predict relative molecular differences, achieving 87% pairwise ranking accuracy and outperforming conventional regression methods.
Problem
Thermal-stability measurements vary across laboratories, limiting reliable prediction from heterogeneous experimental data.
Method
Differential learning models predict relative relationships between molecules using neural networks and computationally derived molecular descriptors.
Results
87% pairwise test-set accuracy demonstrates robust thermal-stability ranking, outperforming conventional regression methods.
Takeaways & Limitations
Differential learning provides useful thermal-stability ranking tools, especially when data are constrained.
Takeaways & Limitations
The curated dataset contains systematic noise, and accounting for intermolecular interactions remains necessary to improve model accuracy.
Abstract
from arXiv · showhide
Predicting thermal stability during handling and storage is essential for the design of safe and reliable energetic materials. However, experimental measurements vary significantly across laboratories due to differences in protocols and analysis methods, making it difficult to train reliable predictive models. We address this challenge through differential learning. Rather than predicting absolute decomposition temperatures, we instead train message passing neural networks to predict relative differences between pairs of molecules. This approach reduces sensitivity to systematic experimental errors and achieves >85% accuracy in ranking compounds by thermal stability, outperforming conventional regression methods on the same heterogeneous dataset. To understand what drives these predictions, we compare neural network models with interpretable alternatives built from descriptors derived from ab initio calculations and cheminformatics software. This analysis identifies bond dissociation enthalpy as a key determinant of thermal stability rankings, providing further insight into the complex chemistry of thermal decomposition. The differential learning framework generalizes across model architectures, from graph neural networks to classical descriptor-based approaches. Our results demonstrate that learning relative properties rather than absolute values offers a practical solution for modeling noisy experimental data, with direct applications in materials design where thermal stability predictions inform safety protocols.
1. Introduction
The introduction presents differential learning as a response to protocol-dependent noise in decomposition-temperature datasets, learning pairwise stability differences instead of absolute temperatures. Applied to CHNO energetic molecules with graph- and descriptor-based models, the framework supports robust ranking and identifies chemically meaningful predictors.
- Motivation and challenge: Decomposition temperature is a proxy for thermal stability, but heating rate, sample mass, thermal contact, and reporting conventions affect measured values.These factors introduce systematic, source-dependent variability into heterogeneous compiled datasets, limiting conventional absolute regression.
- Differential-learning framework: Differential learning predicts pairwise differences between compounds rather than absolute decomposition temperatures, preserving chemically meaningful ordering while attenuating protocol-induced global shifts.The framework is introduced for robust thermal-stability prediction in organic molecules containing only CHNO.
- Modeling strategy: The approach combines message passing neural networks on molecular graphs with differential regressors using cheminformatics and density functional theory descriptors.This design applies differential learning across graph-based and interpretable descriptor-based model architectures.
- Energetic-materials application: Decomposition temperature is a primary metric for safe handling, storage lifetime, and operational reliability in energetic materials, requiring balance between thermal robustness and energetic performance.Insufficient stability can cause premature decomposition, whereas excessive stabilization tends to reduce energetic performance.
- Interpretability and contribution: Feature attribution identifies differences in oxygen balance and bond dissociation enthalpy as top predictors of relative thermal stability, linking model representations to mechanistic concepts.Bond dissociation enthalpy is also described as a mechanistically motivated proxy for thermal robustness.
2. Results and Discussion
Differential learning addresses heterogeneous thermal-decomposition data by predicting pairwise temperature differences rather than absolute values. The resulting models rank compounds accurately while revealing descriptor combinations and structural interactions associated with thermal stability.
- Modeling absolute thermal stability: 48.9 °C MAE and 0.70 R2 were achieved by the best direct-regression model, with accuracy deteriorating at the extremes of the T! distribution.The direct approach used either DFT and cheminformatics descriptors or molecular-graph message passing neural networks.
- Differential model performance: 87% and 86% pairwise accuracy with R2 values of 0.81 and 0.79, respectively, demonstrate strong performance for the two differential models.Both MPNN and RF models outperform random choice even at small ΔT! and converge to 100 % accuracy as ΔT! increases.
- Descriptor interpretation: 13.8 °C mean SHAP value made the difference in oxygen balance (%OB) the most important descriptor, followed by mean BDE at 13.0 °C and minimum BDE at 12.5 °C.The results identify %OB and bond-dissociation descriptors as strong proxies, while the authors caution that BDEs should be combined with other topological and DFT-derived descriptors.
Conclusions
Differential regression models robustly rank molecular thermal stability, achieving state-of-the-art pairwise accuracy while revealing chemical insights. Future work should improve standardized data and incorporate condensed-phase effects.
- Modeling approach: Two differential regression models—a message-passing neural network and descriptor-based random forest—show similar predictive performance and robust ranking metrics.The neural network uses molecular graphs, while the random forest uses interpretable topological and DFT-derived descriptors.
- Performance: 87% pairwise accuracy in the test set establishes state-of-the-art thermal-stability ranking performance for high-throughput energetic-materials discovery.Predictions can also be post-processed to compute classification metrics that further improve ranking accuracy.
- Chemical insights: Differences in oxygen balance and bond dissociation enthalpy are key factors for predicting pairwise thermal-stability differences.For TATB, graph-level SHAP analysis highlights stabilizing hydrogen-bond networks as a structural feature for developing thermally stable materials.
- Interpretation: No individual descriptor should serve as a direct thermal-stability proxy because accurate predictions depend on complex nonlinear relationships among descriptors.Each descriptor contributes little relative to the combined descriptor set.
- Future data resources: A standardized decomposition-temperature database with experimental-condition metadata could reduce protocol and reporting variability, improving training data and future predictive performance.The complete dataset is publicly available for future model development and benchmarking.
- Limitations and future work: Current models omit condensed-phase effects such as intermolecular interactions and crystal packing, motivating future incorporation of calculated and experimental condensed-phase descriptors.Intrinsic molecular features capture a significant fraction of observed behavior, but condensed-phase properties may provide additional predictive information.
4. Methods · Corresponding Authors
The study assembles a heterogeneous decomposition-temperature dataset, computes quantum-chemical and cheminformatics descriptors, and trains differential models to predict pairwise temperature differences. Regression outputs are converted into pairwise classifications and tournament rankings to evaluate relative thermal stability.
- 4.3 Machine learning methods: The Chemprop MPNN treats molecule pairs as disconnected graph components and predicts their decomposition-temperature difference, ∆T_d.The model pools atom- and bond-level information into a molecule-level embedding before feed-forward prediction.
- 4.3 Machine learning methods: 10,000 stratified molecule pairs were sampled across ten temperature bins, with ten repeated splits used for cross-fold validation.The sampling procedure balances pair representation across the range of ∆T_d values.
- 4.3 Machine learning methods: Differential descriptors achieved the best descriptor-model performance and were selected for SHAP analysis after removing zero-variance and highly correlated features.Descriptor models combined DFT, RDKit, and hand-crafted features, while differential regression outperformed classification and standard tree regression criteria outperformed hinge-loss splitting.
- 4.4 Classification and ranking metrics: Pairwise temperature-difference regressions are converted into binary comparisons, where the sign of ∆T_d indicates which molecule is predicted to have the higher decomposition temperature.The hinge loss penalizes incorrect signs, prioritizing pairwise ordering over the magnitude of individual prediction errors.
- 4.4 Classification and ranking metrics: A tournament-based win count ranks test molecules by predicted thermal stability, with pairwise accuracy and Kendall’s tau measuring ordering quality.An anchor-molecule alternative reduces computational scaling from O(N^2) to O(N), but the study uses tournaments for expected robustness against multiple comparisons.