{
  "abstract": "Physics-informed neural networks (PINNs) can solve forward and inverse PDE problems but may struggle with spectral bias and oscillatory, high-frequency, or phase-dependent solutions. We introduce a generalized split complex-valued PINN (SCV-PINN) framework with complex-valued parameters and latent representations. Split activations act separately on real and imaginary components while complex operations preserve their coupling, enabling amplitude--phase representations with practical optimization. Ablation studies evaluate split activation functions and collocation sampling strategies. Forward and inverse benchmarks include the Burgers, Allen--Cahn, Korteweg--de Vries, nonlinear Schrödinger, Helmholtz, and Poisson equations on regular and irregular domains; Kovasznay flow ($\\mathrm{Re}=20$); lid-driven cavity flow ($\\mathrm{Re}=100$); the Lorenz system; and inverse Burgers and Navier--Stokes problems ($\\mathrm{Re}=100$). A three-dimensional Navier--Stokes Beltrami flow further demonstrates applicability to higher-dimensional nonlinear dynamics, with a relative $L_2$ error of $4.07\\times10^{-5}$. Across these tests, SCV-PINN yields high-fidelity solutions and effective parameter identification, improving on real-valued PINNs and selected variants. The results suggest that split complex-valued representations can help address spectral-bias-related difficulties in nonlinear and oscillatory physical systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.15087",
  "author_total": 3,
  "authors": [
    {
      "name": "Biswanath Barman"
    },
    {
      "name": "Rajendra K. Ray"
    },
    {
      "name": "Debdeep Chatterjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ex66er2v0fc36.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.15087",
  "fulltext_url": null,
  "id": "ex66er2v0fc36",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.15087",
  "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",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7169579573",
  "pdf_url": "https://arxiv.org/pdf/2607.15087",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ex66er2v0fc36.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2607.15087",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.15087"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear Partial Differential Equations",
  "title_text": "Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear Partial Differential Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/ex66er2v0fc36",
  "venue": "arXiv",
  "versions": []
}