{
  "abstract": "We analyse inversion of the viscosity ratio M in the Buckley–Leverett equation, distinguishing structural identifiability, observation-operator conditioning, and numerical estimation error. The Riemann solution gives M=4s2−4s from the shock speed s, with relative condition number κ(M)=21+M/(1+M−1), which diverges as M↓0. The continuum physics objective admits exact solution–parameter pairs for every M>0, so identifying the true ratio requires observations. We examine numerical recovery using a viscous physics-informed neural network (PINN) with positive parameterisation and 30 paired repetitions per setting. At M=3, the median parameter error decreases from 514.25% without observations to 6.13% with 25 noisy observations. Additional data decrease the median field error, while median parameter errors are nonmonotone. Over M∈[0.25,10], κ decreases from 18.94 to 2.86, whereas the smooth-branch Cramér–Rao relative scale for 50 scattered observations with 5% Gaussian noise levels off near 7%. Shock crossings supply additional nonregular information. Finite-network physics losses remain small across the tested ratios, with different orderings on training and held-out points. Scalar controls assess finite-resolution viscous-model discrepancy; complementary PINN tests show poorer recovery as the front sharpens. Recovery accuracy therefore depends jointly on the observation operator, regularisation, and numerical estimator.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Computer Science, Al-Farabi Kazakh National University, 71 Al-Farabi Avenue, Almaty 050040, Kazakhstan",
    "Department of Television and Media Technologies, Tashkent University of Information Technologies Named After Muhammad Al-Khwarizmi, 108 Amir Temur Avenue, Tashkent 100200, Uzbekistan",
    "Department of Computer Science, Addis Ababa University, Addis Ababa P.O. Box 1176, Ethiopia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Samson Dawit Bekele",
      "orcid": "0009-0005-9719-4343"
    },
    {
      "affs": [
        0
      ],
      "name": "Yerzhan Kenzhebek",
      "orcid": "0000-0002-6492-8292"
    },
    {
      "affs": [
        0
      ],
      "name": "Saltanbek Mukhambetzhanov",
      "orcid": "0000-0003-1335-7319"
    },
    {
      "affs": [
        1
      ],
      "name": "Saida Tastanova",
      "orcid": "0000-0001-5948-8205"
    },
    {
      "affs": [
        2
      ],
      "name": "Dagmawi Lemma",
      "orcid": "0000-0002-1647-5188"
    },
    {
      "affs": [
        0
      ],
      "name": "Timur Imankulov",
      "orcid": "0000-0002-8865-3676"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3w974t2vcdpdk.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193575",
  "fulltext_url": null,
  "id": "3w974t2vcdpdk",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3575",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7215903350",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/3w974t2vcdpdk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193575",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3575"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Model Reduction and Neural Networks",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Identifiability and Conditioning of Flux-Parameter Inversion for the Buckley–Leverett Equation",
  "title_text": "Identifiability and Conditioning of Flux-Parameter Inversion for the Buckley–Leverett Equation",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/3w974t2vcdpdk",
  "venue": "Mathematics",
  "versions": []
}