AI neural network ranks structural descriptors for supercooled water, identifies top performers
By Marie
Water in its supercooled state, liquid below the freezing point, is one of the most studied and least understood substances in physics. At low temperatures, it is thought to exist in two distinct liquid forms: a low-density liquid (LDL) with an open, tetrahedral structure and a high-density liquid (HDL) with a more compact arrangement. The structural features that best distinguish these two forms have been debated for decades.
A team at the University of Osaka, led by Kang Kim and Nobuyuki Matubayasi of the Graduate School of Engineering Science, has now used a fully connected neural network to resolve the debate, not by simulating water itself, but by asking the AI which structural descriptors best discriminate between water’s two liquid phases. The results, published July 6 in Communications Chemistry, rank 16 candidate descriptors and identify the clear winners.
The challenge of supercooled water
Water can remain liquid far below its freezing point, down to approximately 230 K at atmospheric pressure, provided it is free of impurities that would trigger ice nucleation. In this supercooled regime, water’s properties change dramatically: density, heat capacity, and compressibility all exhibit anomalous behavior. The prevailing hypothesis is that these anomalies reflect the existence of a liquid-liquid critical point (LLCP) deep in the supercooled region, below which two distinct liquid phases, LDL and HDL, coexist.
But experimentally accessing this region is extraordinarily difficult. Below roughly 230 K, water crystallizes too quickly for meaningful measurements. Molecular dynamics simulations with accurate water models (the team used TIP4P/2005 in GROMACS) provide a window into this inaccessible regime, but the structural differences between LDL and HDL are subtle, too subtle for simple visual analysis of simulation snapshots.
The neural network approach
The team trained a fully connected neural network implemented in TensorFlow to classify water configurations by temperature, using as input one of 16 structural descriptors at a time. The logic: a descriptor that enables the network to accurately classify temperature is one that captures the structural changes that distinguish HDL from LDL.
The network architecture was deliberately simple: an input layer of 1,000 nodes (one per water molecule, each receiving that molecule’s descriptor value), a single hidden layer of 1,000 nodes with LeakyReLU activation, and a sigmoid output for binary temperature classification. For each descriptor, the network was trained on 15 temperature pairs spanning 200 K to 300 K, in both isochoric and isobaric ensembles, and performance was measured by AUC (area under the ROC curve).
Logistic regression was also run on the same data to distinguish linear from nonlinear discriminative power. LIME (Local Interpretable Model-Agnostic Explanations) was applied to the top four descriptors to verify that the network learned physically meaningful relationships.
The ranking
The 16 descriptors fell into four performance tiers:
| Tier | AUC range | Descriptors |
|——|———–|————-|
| Excellent (≥0.9) | 0.957–0.998 | LSI (Local Structure Index), ζ (zeta), NTCₕᵦ (H-bond network communicability), Nₕᵦ (H-bond count) |
| Good (0.75–0.9) |, | Tetrahedral order (qₜₑₜ, qₙ), V₄₋₅ (energy difference), coordination number, V₄, Q₄ |
| Moderate (0.65–0.75) |, | Ψ, d₅, Voronoi volume, V₅ |
| Poor (<0.65) |, | NTC (distance-based communicability), Q₆ |
The top performer, LSI, achieved a near-perfect AUC of 0.998, meaning it alone contains essentially all the structural information needed to distinguish HDL from LDL. LSI measures the gap between a water molecule’s first and second coordination shells. Its close competitor ζ (AUC 0.970) quantifies the difference between the nearest non-hydrogen-bonded neighbor distance and the farthest hydrogen-bonded neighbor distance. Both describe, in slightly different ways, how open or compact a molecule’s local environment is.
The H-bond network topology descriptors, NTCₕᵦ and Nₕᵦ, formed a complementary group, capturing structural information independent of LSI and ζ. Notably, their strong performance depended on nonlinearity: logistic regression gave them much lower AUC values, confirming the neural network’s ability to exploit nonlinear relationships was essential for these descriptors.
What this means
The finding has practical implications. The four top-ranked descriptors, LSI, ζ, NTCₕᵦ, and Nₕᵦ, can now be used with confidence in future studies of supercooled water, reducing the need to compute all 16 candidates. The near-perfect performance of LSI also suggests that the gap between the first and second coordination shells is, structurally speaking, the essence of the HDL-LDL distinction.
More broadly, the study demonstrates a methodology for ranking structural descriptors in complex liquids using machine learning as an objective evaluator, an approach that could be extended to other glass-forming liquids, ionic liquids, and aqueous solutions where the relevant structural features remain contested.
The work was supported by JSPS KAKENHI, MEXT, and JST.
Sources:
1. Yoshikawa, K., Shikata, K., Kim, K. & Matubayasi, N. “Machine learning evaluation of structural descriptors for supercooled water.” Communications Chemistry 9, 217 (2026). DOI: 10.1038/s42004-026-02097-1
2. Also on arXiv: 2605.00415 [cond-mat.soft]
3. University of Osaka press release via EurekAlert, July 2026.