Metraipolis › archive › dc_bcfd5e802a4e

Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks — arXiv:2609.01558

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.01558
License (as archived): CC0-1.0
Archived: 2026-10-17T06:52:26.265Z
SHA-256 of the archived text: 5907641014e979c5658487a9a46e78669a24929ba96a8673ce9734bd07b6857c
Stable URL of this page: https://metraipolis.com/documento/dc_bcfd5e802a4e

How to cite

Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks — arXiv:2609.01558 — arXiv (en), https://arxiv.org/abs/2609.01558 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bcfd5e802a4e (Metraipolis archive dc_bcfd5e802a4e, sha256 5907641014e979c5658487a9a46e78669a24929ba96a8673ce9734bd07b6857c)

BibTeX

@misc{dcbcfd5e802a4e,
  title = {Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks — arXiv:2609.01558},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.01558},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bcfd5e802a4e; sha256 5907641014e979c5658487a9a46e78669a24929ba96a8673ce9734bd07b6857c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.01558. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Training Physics-Informed Neural Networks (PINNs) requires jointly optimizing physics residual and initial/boundary condition loss terms, which often induce conflicting gradients. Gradient surgery methods mitigate this issue by constructing directions from loss-specific gradients to reduce conflict before optimizer transformation. However, even when the constructed direction is conflict-free, this property may not be preserved after optimizer transformation. Let $a_t$ denote the direction constructed by gradient surgery, $u_t$ the optimizer proposal, and $\mathcal{C}_t$ the conflict-free cone induced by the loss-specific gradients. We show that modern optimizers can transform $a_t$ through mechanisms such as historical state, adaptive scaling, preconditioning, or decoupled weight decay, so $a_t \in \mathcal{C}_t$ does not generally imply $u_t \in \mathcal{C}_t$. We refer to this optimizer-induced discrepancy in conflict-freeness between $a_t$ and $u_t$ as Gradient-Update Mismatch (GUM). Accordingly, we propose Gradient-Update Alignment (GUA), which projects $u_t$ onto $\mathcal{C}_t$ to obtain the aligned update $p_t$ and applies $p_t$ to the parameters. When the optimizer maintains internal state, GUA further adjusts this state toward targets reconstructed from the applied update. We conduct extensive experiments and find that GUM is widespread across momentum, adaptive, and curvature-based optimizers, with conflict rates reaching up to 86.3%. Across all PINN settings, GUA achieves conflict-free applied updates and consistently improves various gradient surgery methods, reducing the relative $L_2$ error by up to 98.2% in individual settings. Data and code are available at this https URL .

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-02 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.01558 — 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 2026-10-17T06:41:55.868Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).