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DeSyR: A Decoupled Symbolic Recovery Framework with PINN-Guided Structure Search and Physics-Informed Coefficient Refinement — arXiv:2609.00530

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.00530
License (as archived): CC0-1.0
Archived: 2026-10-17T06:52:07.715Z
SHA-256 of the archived text: 7f5e6aa717982ed2f5cf0c818c79ee717a94295734dc43832ef36c8f672f4d4b
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How to cite

DeSyR: A Decoupled Symbolic Recovery Framework with PINN-Guided Structure Search and Physics-Informed Coefficient Refinement — arXiv:2609.00530 — arXiv (en), https://arxiv.org/abs/2609.00530 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7bee2eec1fa0 (Metraipolis archive dc_7bee2eec1fa0, sha256 7f5e6aa717982ed2f5cf0c818c79ee717a94295734dc43832ef36c8f672f4d4b)

BibTeX

@misc{dc7bee2eec1fa0,
  title = {DeSyR: A Decoupled Symbolic Recovery Framework with PINN-Guided Structure Search and Physics-Informed Coefficient Refinement — arXiv:2609.00530},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.00530},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7bee2eec1fa0; sha256 7f5e6aa717982ed2f5cf0c818c79ee717a94295734dc43832ef36c8f672f4d4b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.00530. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Recovering compact explicit solutions from neural approximations is challenging when imperfect teacher data guide symbolic topology search and coefficient estimation. We present DeSyR, a decoupled symbolic recovery framework for differential equations. A physics-informed neural network guides repeated searches to construct candidate topologies with provisional constants. Once a topology is fixed, its coefficients are refined solely from the governing equation and prescribed constraints, followed by gated selection and verification. For linear fixed-topology parameterizations, we characterize teacher-error inheritance and show that finite-weight mixed data--physics fitting retains an $O(\beta^{-1})$ teacher-dependent contribution when the teacher error projects onto the model space. Under well-posedness, representability, zero-residual attainment, and discrete determinacy, physics-only refinement conditionally recovers exact coefficients; for nonlinear parameterizations, the corresponding guarantees are local. DeSyR is evaluated on 15 differential-equation problems across 18 configurations covering high-order, space--time, multidimensional, nonlinear, and coupled systems. A candidate-level audit yields a 99.23% convergence rate among free-parameter refits, while every selected refinement involving free coefficients converges. Configuration-level median refined relative $L_2$ errors are $2.31\times10^{-14}$ or lower. In same-topology comparisons, refinement reduces error by eight to fourteen orders of magnitude. These results show that an approximate neural teacher can guide topology discovery without imposing its error scale on final recovered coefficients, provided a target-capable topology is retained and physics-only refinement converges.

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/2609.00530 — 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 2026-10-17T06:41:55.796Z 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).