{
  "abstract": "In molecular machine learning (ML), significant progress has been made on integrating fundamental thermodynamic relations into ML models. Such physics-informed approaches can be categorized as hard-constrained, where the thermodynamic relations are embedded in the model architecture, and soft-constrained, where relations are included in the training loss. While both approaches have been applied to various property prediction tasks, a systematic comparison on experimental data is lacking. We herein compare hard- and soft-constrained approaches on a numerically challenging case study: the prediction of vapor pressure, saturated liquid and vapor molar volumes, and enthalpy of vaporization as functions of temperature for single-species vapor-liquid equilibrium, related by the exact Clapeyron equation. Furthermore, soft-constrained approaches in molecular ML typically balance data and physics losses with a fixed weighting factor, requiring careful tuning. To overcome this, we investigate the augmented Lagrangian method (ALM), well established in constrained optimization. We find that for the soft-constrained approach, using the ALM improves prediction performance in terms of constraint satisfaction by factor 2 and reduces training epochs compared to using a fixed penalty by 30%. Hence, in the soft-constrained approach, the use of the ALM is always recommended. The hard-constrained approach, which entails additional architectural design choices, can reach on par accuracy with the soft-constrained approach, at even higher thermodynamic consistency, reaching 12 orders of magnitude closer approximation of the Clapeyron equation. Overall, the hard-constrained approach is most promising when thermodynamic consistency is critical, yet requires tailoring the ML model architecture to the respective thermodynamic relation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36947",
  "author_total": 3,
  "authors": [
    {
      "name": "Jan Pavšek"
    },
    {
      "name": "Jan G. Rittig"
    },
    {
      "name": "Alexander Mitsos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6a6z77ahpt0pr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36947",
  "fulltext_url": null,
  "id": "6a6z77ahpt0pr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36947",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "2505|Machine Learning in Materials Science"
    ]
  ],
  "openalex": "W7214996885",
  "pdf_url": "https://arxiv.org/pdf/2609.36947",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6a6z77ahpt0pr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36947",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36947"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "A systematic comparison of hard- and soft-constrained physics-informed molecular machine learning with the Clapeyron equation",
  "title_text": "A systematic comparison of hard- and soft-constrained physics-informed molecular machine learning with the Clapeyron equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/6a6z77ahpt0pr",
  "venue": "arXiv",
  "versions": []
}