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Cautious Conflict-Free Inverse Gradient Methods — arXiv:2610.31855

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.31855
License (as archived): CC0-1.0
Archived: 2026-10-26T20:11:27.591Z
SHA-256 of the archived text: 62aefec9fb8a78154a8cbc27ba460ab7b9cc51565eb8ad690fa27c6cdb1fd6e8
Stable URL of this page: https://metraipolis.com/documento/dc_ff2c4423930d

How to cite

Cautious Conflict-Free Inverse Gradient Methods — arXiv:2610.31855 — arXiv (en), https://arxiv.org/abs/2610.31855 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ff2c4423930d (Metraipolis archive dc_ff2c4423930d, sha256 62aefec9fb8a78154a8cbc27ba460ab7b9cc51565eb8ad690fa27c6cdb1fd6e8)

BibTeX

@misc{dcff2c4423930d,
  title = {Cautious Conflict-Free Inverse Gradient Methods — arXiv:2610.31855},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.31855},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ff2c4423930d; sha256 62aefec9fb8a78154a8cbc27ba460ab7b9cc51565eb8ad690fa27c6cdb1fd6e8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.31855. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Partial differential equations (PDEs) are indispensable tools for modeling complex phenomena in physics and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful alternative to traditional numerical solvers by directly incorporating physical constraints into neural network loss functions. Despite their advantages, PINN training requires multi-objective optimization, which often leads to significant gradient conflicts among boundary, initial, and residual loss terms. The Conflict-Free Inverse Gradient (ConFIG) method addresses these conflicts; however, integrating ConFIG with adaptive optimizers such as Adam introduces a critical vulnerability: the conflict-free direction generated by ConFIG is further processed by the optimizer, and the resulting weight update may no longer be conflict-free with respect to the task gradients. To address this issue, Cautious ConFIG is proposed as a concise three-line extension to the ConFIG algorithm that empirically restores the conflict-freeness guarantee prior to the weight update. The method is evaluated on three PINN benchmarks: the 1D Viscous Burgers' equation, the 1D Nonlinear Schrödinger equation, and the 2D Kovasznay flow. Experimental results demonstrate consistent performance improvements over the standard ConFIG baseline. Additionally, the stabilizing effect of cautious masking and its reaction to conflict severity, task number, and optimizer lag are investigated using a simple toy system.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.31855 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-26T19:49:03.364Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).