Physics-Constrained Neural ODEs for MXene Bandgap Prediction with Conformal Uncertainty.
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| Title: | Physics-Constrained Neural ODEs for MXene Bandgap Prediction with Conformal Uncertainty. |
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| Authors: | Kati, Nida1 (AUTHOR), Ucar, Ferhat2 (AUTHOR) fucar@firat.edu.tr |
| Source: | Nanomaterials (2079-4991). Jun2026, Vol. 16 Issue 11, p673. 30p. |
| Subjects: | Prediction models, Band gaps, Photocatalysis, Uncertainty (Information theory) |
| Abstract: | Two-dimensional transition metal carbides and nitrides, known collectively as MXenes, are attractive photocatalyst candidates because their surface chemistry and atomic composition can be tuned over a wide compositional window. A crucial design quantity is the electronic bandgap, which selects whether a given MXene couples with solar radiation and aligns with the redox levels of water splitting. High-fidelity bandgap calculations using the PBE0 hybrid functional are computationally expensive, which has motivated several machine learning surrogates. To the best of our knowledge, this is the first study to integrate a continuous-depth Neural Ordinary Differential Equation backbone with multi-fidelity Δ learning, distribution-free split-conformal calibration, and uncertainty-aware Pareto screening into a single mathematically grounded pipeline for MXene bandgap prediction. In this work, we develop a physics-constrained neural ordinary differential equation (PC-NODE) that predicts MXene bandgaps from a compact 34-dimensional descriptor set, without relying on the density of states. The model couples a classifier head for the metal/semiconductor decision with a regression head for the gap magnitude, and enforces three physically motivated properties: non-negativity of the predicted gap and monotonicity between the low-fidelity Perdew–Burke–Ernzerhof (PBE) and the high-fidelity PBE0 estimates are obtained exactly through a softplus-parameterised Δ learning construction, while a hurdle coupling that drives metal predictions towards zero is enforced via a quadratic penalty and verified empirically. In short, two of the three physical constraints are guaranteed by construction, and the third is approximately enforced and verified empirically; the same distinction is maintained consistently in the methodology, the constraint audit and the conclusion. Trained on the 4356-structure MXgap database, a ten-seed ensemble reaches a mean absolute error of 0.186 eV (per-seed 0.206 ± 0.006 eV) and a coefficient of determination R 2 = 0.880 on the semiconductor test subset, with a classifier accuracy of 0.856 and a Receiver Operating Characteristic Area Under the Curve (ROC-AUC) of 0.925 . A split-conformal calibration step then delivers prediction intervals whose empirical coverage matches the 90% target within 0.5 percentage points. Finally, an uncertainty-aware Pareto screening step applies the trained surrogate to a held-out subset of 396 lanthanum-based MXenes and identifies 74 candidates inside the photocatalytic water splitting window [1.23, 3.10] eV. The framework offers a mathematically grounded, data-efficient alternative to feature-heavy pipelines and is reproducible from the open MXgap resource. [ABSTRACT FROM AUTHOR] |
| Copyright of Nanomaterials (2079-4991) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: Physics-Constrained Neural ODEs for MXene Bandgap Prediction with Conformal Uncertainty. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kati%2C+Nida%22">Kati, Nida</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ucar%2C+Ferhat%22">Ucar, Ferhat</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> fucar@firat.edu.tr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Nanomaterials+%282079-4991%29%22">Nanomaterials (2079-4991)</searchLink>. Jun2026, Vol. 16 Issue 11, p673. 30p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Prediction+models%22">Prediction models</searchLink><br /><searchLink fieldCode="DE" term="%22Band+gaps%22">Band gaps</searchLink><br /><searchLink fieldCode="DE" term="%22Photocatalysis%22">Photocatalysis</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty+%28Information+theory%29%22">Uncertainty (Information theory)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Two-dimensional transition metal carbides and nitrides, known collectively as MXenes, are attractive photocatalyst candidates because their surface chemistry and atomic composition can be tuned over a wide compositional window. A crucial design quantity is the electronic bandgap, which selects whether a given MXene couples with solar radiation and aligns with the redox levels of water splitting. High-fidelity bandgap calculations using the PBE0 hybrid functional are computationally expensive, which has motivated several machine learning surrogates. To the best of our knowledge, this is the first study to integrate a continuous-depth Neural Ordinary Differential Equation backbone with multi-fidelity Δ learning, distribution-free split-conformal calibration, and uncertainty-aware Pareto screening into a single mathematically grounded pipeline for MXene bandgap prediction. In this work, we develop a physics-constrained neural ordinary differential equation (PC-NODE) that predicts MXene bandgaps from a compact 34-dimensional descriptor set, without relying on the density of states. The model couples a classifier head for the metal/semiconductor decision with a regression head for the gap magnitude, and enforces three physically motivated properties: non-negativity of the predicted gap and monotonicity between the low-fidelity Perdew–Burke–Ernzerhof (PBE) and the high-fidelity PBE0 estimates are obtained exactly through a softplus-parameterised Δ learning construction, while a hurdle coupling that drives metal predictions towards zero is enforced via a quadratic penalty and verified empirically. In short, two of the three physical constraints are guaranteed by construction, and the third is approximately enforced and verified empirically; the same distinction is maintained consistently in the methodology, the constraint audit and the conclusion. Trained on the 4356-structure MXgap database, a ten-seed ensemble reaches a mean absolute error of 0.186 eV (per-seed 0.206 ± 0.006 eV) and a coefficient of determination R 2 = 0.880 on the semiconductor test subset, with a classifier accuracy of 0.856 and a Receiver Operating Characteristic Area Under the Curve (ROC-AUC) of 0.925 . A split-conformal calibration step then delivers prediction intervals whose empirical coverage matches the 90% target within 0.5 percentage points. Finally, an uncertainty-aware Pareto screening step applies the trained surrogate to a held-out subset of 396 lanthanum-based MXenes and identifies 74 candidates inside the photocatalytic water splitting window [1.23, 3.10] eV. The framework offers a mathematically grounded, data-efficient alternative to feature-heavy pipelines and is reproducible from the open MXgap resource. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Nanomaterials (2079-4991) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3390/nano16110673 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 30 StartPage: 673 Subjects: – SubjectFull: Prediction models Type: general – SubjectFull: Band gaps Type: general – SubjectFull: Photocatalysis Type: general – SubjectFull: Uncertainty (Information theory) Type: general Titles: – TitleFull: Physics-Constrained Neural ODEs for MXene Bandgap Prediction with Conformal Uncertainty. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kati, Nida – PersonEntity: Name: NameFull: Ucar, Ferhat IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 20794991 Numbering: – Type: volume Value: 16 – Type: issue Value: 11 Titles: – TitleFull: Nanomaterials (2079-4991) Type: main |
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