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arxiv: 2604.11660 · v1 · submitted 2026-04-13 · ❄️ cond-mat.mtrl-sci · physics.data-an

A unified descriptor framework for hydrogen storage capacity and equilibrium pressure in interstitial hydrides

Seong-Hoon Jang , Di Zhang , Xue Jia , Hung Ba Tran , Linda Zhang , Ryuhei Sato , Yusuke Hashimoto , Yusuke Ohashi
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Toyoto Sato Kiyoe Konno Shin-ichi Orimo Hao Li
This is my paper

Pith reviewed 2026-05-10 15:13 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.data-an
keywords interstitial hydrideshydrogen storagesymbolic regressiondescriptorsatomic radiusshear modulusequilibrium pressuremetal hydrides
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The pith

Separate physical descriptors govern hydrogen storage capacity versus equilibrium pressure in interstitial hydrides

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies white-box symbolic regression to a database of pressure-composition-temperature data for interstitial hydrides to extract interpretable relationships between averaged material properties and two target performance metrics. It finds that storage capacity depends on geometric and lattice factors captured by average metal atomic radius and thermal conductivity, with a preferred window near 1.47 Å and relatively low conductivity. Equilibrium pressure at room temperature instead tracks elastic properties through average shear modulus and Poisson's ratio, which encode lattice rigidity and compliance. Because the two properties respond to largely orthogonal descriptor sets, compositional changes can be chosen to raise capacity while holding pressure near practical values around 0.1 MPa. A reader would care because the separation supplies concrete, testable rules for alloy design rather than opaque correlations.

Core claim

Using a curated database of pressure-composition-temperature measurements and white-box symbolic regression, the analysis reveals a clear separation of governing mechanisms, in which w is governed by geometric and lattice conditions, captured by the average atomic radius (⟨r_M⟩) and average thermal conductivity (⟨κ⟩), with an optimal regime of r_M ∼ 1.47 Å and relatively low ⟨κ⟩. In contrast, P_eq,RT is governed by elastic properties, captured by the average shear modulus (⟨G⟩) and average Poisson's ratio (⟨ν⟩), reflecting the role of lattice rigidity and mechanical compliance. These relationships are translated into compositional optimization pathways that follow the descriptor trends above

What carries the argument

White-box symbolic regression that isolates distinct averaged-property descriptor pairs for capacity (geometric/lattice) versus pressure (elastic), enabling direct compositional mapping

If this is right

  • Compositional pathways can be followed to increase storage capacity w while maintaining equilibrium pressure near 0.1 MPa at room temperature
  • Candidate alloys can be screened or designed by targeting the identified optimal ranges for radius, conductivity, shear modulus, and Poisson ratio
  • The same descriptor separation supplies a template for physics-informed optimization of other interstitial compounds
  • The framework yields an interpretable, general strategy for designing energy-storage materials without black-box models

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same separation of geometric versus elastic controls may appear in related interstitial systems such as nitride or carbide hosts for other gases
  • High-throughput computational screening that enforces the 1.47 Å radius window could rapidly generate new test compositions
  • If the radius optimum proves robust, it would constrain the periodic-table search space for future hydride discovery campaigns

Load-bearing premise

The assumption that the symbolic regression results reflect underlying physical mechanisms rather than statistical correlations in the specific dataset, and that the optimal regimes identified will generalize to new compositions

What would settle it

Synthesis and PCT measurement of an interstitial hydride alloy tuned to average metal radius near 1.47 Å and low thermal conductivity yet outside the suggested elastic-property window, checking whether capacity fails to rise while pressure remains near 0.1 MPa

read the original abstract

Hydrogen is a promising energy carrier, yet its practical deployment is limited by the lack of storage materials that simultaneously achieve high storage capacity ($w$) and practical equilibrium pressure at room temperature ($P_{\rm eq,RT}$). Interstitial metal hydrides offer fast kinetics and favorable thermodynamics (high $P_{\rm eq,RT}$) but suffer from intrinsically low w. Here, we establish a physically interpretable, data-driven framework to uncover descriptor-property relationships in interstitial hydrides using a curated database of pressure-composition-temperature measurements (Digital Hydrogen Platform, DigHyd) and white-box symbolic regression. Strikingly, the analysis reveals a clear separation of governing mechanisms, in which $w$ is governed by geometric and lattice conditions, captured by the average atomic radius ($\left\langle r_M \right\rangle$) and average thermal conductivity ($\left\langle\kappa\right\rangle$), with an optimal regime of $r_M \sim 1.47 \r{A}$ and relatively low $\left\langle\kappa\right\rangle$. In contrast, $P_{\rm eq,RT}$ is governed by elastic properties, captured by the average shear modulus ($\left\langle G \right\rangle$) and average Poisson's ratio ($\left\langle \nu \right\rangle$), reflecting the role of lattice rigidity and mechanical compliance. These relationships are translated into compositional optimization pathways that follow the descriptor trends above, enabling the design of candidate materials with enhanced w under practical equilibrium conditions ($P_{\rm eq,RT} \sim 0.1$ MPa). This work establishes a general, interpretable strategy for physics-informed design of energy materials systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a data-driven framework for interstitial hydrides that uses white-box symbolic regression on the DigHyd database of pressure-composition-temperature data to identify descriptors for hydrogen storage capacity w and room-temperature equilibrium pressure P_eq,RT. It reports a separation in which w is controlled by geometric/lattice factors (average atomic radius ⟨r_M⟩ with optimum ~1.47 Å and average thermal conductivity ⟨κ⟩) while P_eq,RT is controlled by elastic factors (average shear modulus ⟨G⟩ and average Poisson's ratio ⟨ν⟩), and translates these into compositional design pathways aimed at simultaneous improvement of both properties.

Significance. If the reported descriptor separation proves robust and generalizable, the work would supply an interpretable, physics-informed route to hydride optimization that could help resolve the capacity-pressure trade-off in hydrogen storage. The explicit use of symbolic regression for transparency is a methodological strength. The significance is currently limited by the absence of independent validation that would distinguish physical mechanisms from statistical associations within the specific dataset.

major comments (2)
  1. [Abstract] Abstract: the claim of a 'clear separation of governing mechanisms' is load-bearing for the central contribution, yet the descriptors and optimal regimes (e.g., r_M ∼ 1.47 Å) are obtained directly from symbolic regression fits to DigHyd; without reported out-of-sample tests, ablation against alternative descriptor sets, or multicollinearity diagnostics among the averaged elemental properties, the mechanistic interpretation risks circularity.
  2. [Results] Results section on symbolic regression: the separation between geometric/lattice descriptors for w and elastic descriptors for P_eq,RT is presented as physically meaningful, but the manuscript does not provide the regression objective function, feature-importance ranking, or cross-validation metrics that would demonstrate the separation is not an artifact of the composition distribution in the database.
minor comments (2)
  1. [Notation] The averaging brackets ⟨ ⟩ for elemental properties should be defined at first use and the procedure for computing averages from elemental tables should be stated explicitly.
  2. [Figures] Any figures displaying regression surfaces or descriptor distributions would benefit from inclusion of quantitative goodness-of-fit statistics (R², MAE, or cross-validation scores) to allow readers to assess the strength of the reported relationships.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify the need for greater transparency and validation in our symbolic regression analysis to support the claimed separation of mechanisms. We have prepared revisions that directly address these points by adding the requested methodological details, validation metrics, and diagnostics. These changes will be incorporated into the revised manuscript to strengthen the robustness of our conclusions without altering the core findings.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of a 'clear separation of governing mechanisms' is load-bearing for the central contribution, yet the descriptors and optimal regimes (e.g., r_M ∼ 1.47 Å) are obtained directly from symbolic regression fits to DigHyd; without reported out-of-sample tests, ablation against alternative descriptor sets, or multicollinearity diagnostics among the averaged elemental properties, the mechanistic interpretation risks circularity.

    Authors: We agree that explicit validation is required to substantiate the mechanistic interpretation and to rule out circularity. In the revised manuscript we will add: (i) out-of-sample testing via a 70/30 train/test split of the DigHyd database with reported R² and RMSE on the held-out set; (ii) ablation experiments comparing the selected descriptor sets against alternative feature pools (e.g., replacing averaged elemental properties with composition-weighted alternatives); and (iii) multicollinearity diagnostics (variance inflation factors and pairwise correlation matrices) for the averaged properties ⟨r_M⟩, ⟨κ⟩, ⟨G⟩ and ⟨ν⟩. These additions will be placed in a new subsection of Results and referenced in the Abstract to support the separation claim. revision: yes

  2. Referee: [Results] Results section on symbolic regression: the separation between geometric/lattice descriptors for w and elastic descriptors for P_eq,RT is presented as physically meaningful, but the manuscript does not provide the regression objective function, feature-importance ranking, or cross-validation metrics that would demonstrate the separation is not an artifact of the composition distribution in the database.

    Authors: We acknowledge that these implementation details were omitted and that their absence leaves open the possibility of database-specific artifacts. The revised manuscript will include a dedicated “Symbolic Regression Methodology” subsection that specifies: the objective function (mean-squared error plus complexity penalty as implemented in the PySR library), feature-importance ranking derived from the frequency of each descriptor across the Pareto-optimal expressions, and k-fold (k=5) cross-validation scores with standard deviations. We will also report the distribution of training compositions to allow readers to assess potential bias. These additions will demonstrate that the geometric-versus-elastic separation persists under cross-validation and is not an artifact of the database composition. revision: yes

Circularity Check

0 steps flagged

Data-driven symbolic regression yields empirical descriptor trends; derivation is self-contained without reduction to inputs by construction

full rationale

The paper explicitly frames its contribution as a data-driven analysis: white-box symbolic regression is applied to the DigHyd database of PCT measurements to extract averaged elemental descriptors (⟨r_M⟩, ⟨κ⟩ for w; ⟨G⟩, ⟨ν⟩ for P_eq,RT) and identify an optimal regime. The claimed 'separation of governing mechanisms' and subsequent compositional optimization pathways are direct outputs of this regression rather than prior assumptions or self-referential definitions. No equations, uniqueness theorems, or ansatzes are imported via self-citation in a load-bearing way; the framework does not claim first-principles derivation but presents statistical relationships from the specific dataset as interpretable trends. Design suggestions follow the fitted descriptor trends by construction of the method, which is the standard and non-circular use of such models. The analysis is therefore self-contained as an empirical discovery procedure.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims depend on data-fitted parameters from regression and assumptions about the database and method's ability to reveal mechanisms; no first-principles derivations or external validations are mentioned.

free parameters (2)
  • optimal average atomic radius r_M = 1.47 Å
    Determined as optimal regime from the symbolic regression analysis on the DigHyd database.
  • low average thermal conductivity threshold
    Selected based on observed trends in the data for high w.
axioms (2)
  • domain assumption White-box symbolic regression can extract physically meaningful descriptors from property data
    Central to the framework's interpretability claim.
  • domain assumption The Digital Hydrogen Platform (DigHyd) database accurately represents interstitial hydride behaviors
    Basis for all analysis and relationships derived.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Building a physics-aware AI ecosystem for solid-state hydrogen storage materials

    cond-mat.mtrl-sci 2026-05 unverdicted novelty 4.0

    A proposed physics-aware AI ecosystem combines organized data, physics-based models, and experimental feedback loops to enable consistent optimization and discovery of hydrogen storage materials.

Reference graph

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