{
  "abstract": "Transport models underpin the design and optimisation of chemical processes, yet their constitutive laws are typically hand-picked, their experimental initial conditions are assumed exact, and their computational cost restricts optimisation to a handful of process variables. Here we introduce a differentiable hybrid modelling framework that embeds neural networks within a GPU-accelerated population balance equation solver to discover constitutive laws and assimilate initial conditions directly from experimental crystallisation data. Using thirteen real experiments with multi-dimensional size and shape measurements, we show that treating measured initial conditions as exact yields a physically inconsistent rate law despite improved predictive accuracy, whereas assimilating them recovers a physically consistent, non-linear law and reduces trajectory error sevenfold relative to conventional modelling. End-to-end differentiability further enables gradient-based optimisation of high-dimensional operating profiles, identifying a 300-variable temperature profile that reduces crystal aspect ratio by 25% at constant mass, facilitating superior product attributes. Our framework augments, rather than replaces, mechanistic modelling, offering a general route to learning transport models from data and optimising processes with them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04011",
  "author_total": 4,
  "authors": [
    {
      "name": "Arthur Jessop"
    },
    {
      "name": "Mohammed Alsubeihi"
    },
    {
      "name": "Ben Moseley"
    },
    {
      "name": "Ashwin Kumar Rajagopalan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e1frkqp1mv5qp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04011",
  "fulltext_url": null,
  "id": "e1frkqp1mv5qp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04011",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7208739881",
  "pdf_url": "https://arxiv.org/pdf/2609.04011",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e1frkqp1mv5qp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2609.04011",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04011"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data",
  "title_text": "Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/e1frkqp1mv5qp",
  "venue": "arXiv",
  "versions": []
}