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Hyperparameter selection for equation learning with biologically-informed neural networks — arXiv:2610.02954

Source: arXiv
Original: https://arxiv.org/abs/2610.02954
License (as archived): CC0-1.0
Archived: 2026-10-05T23:10:01.445Z
SHA-256 of the archived text: 7977630f50757664de3f5208d60afee5ea6b221cce621fa190d964ea5bbb9e04
Stable URL of this page: https://metraipolis.com/documento/dc_023fc072e702

How to cite

Hyperparameter selection for equation learning with biologically-informed neural networks — arXiv:2610.02954 — arXiv, https://arxiv.org/abs/2610.02954 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_023fc072e702 (Metraipolis archive dc_023fc072e702, sha256 7977630f50757664de3f5208d60afee5ea6b221cce621fa190d964ea5bbb9e04)

BibTeX

@misc{dc023fc072e702,
  title = {Hyperparameter selection for equation learning with biologically-informed neural networks — arXiv:2610.02954},
  howpublished = {arXiv},
  url = {https://arxiv.org/abs/2610.02954},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_023fc072e702; sha256 7977630f50757664de3f5208d60afee5ea6b221cce621fa190d964ea5bbb9e04},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv, https://arxiv.org/abs/2610.02954. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Biologically-informed neural networks (BINNs) have emerged as a flexible subclass of physics-informed neural networks (PINNs) for learning terms in partial differential equations from data. BINNs are particularly suited for biological systems, where the governing equations are highly nonlinear and only partially known a priori, and where data observations are often sparse, noisy, and incomplete. However, applying BINNs effectively in practice depends critically on hyperparameter selection, which remains a central challenge in equation-learning frameworks. Hyperparameters are often chosen heuristically and only cursorily documented, which limits the reproducibility of results and the transferability of methods. We present a diagnostic workflow for hyperparameter selection that can be used when the ground-truth equations are not known. The workflow is guided by three main questions: (1) Are the benefits of greater network capacity worth the cost? (2) Do more training epochs keep reducing the validation loss? (3) Do the learned terms stop changing as network capacity and training increase? We apply our workflow to synthetic systems of varying complexity with known ground truth, spanning diffusion and growth right-hand side terms and data ranging from 1D+t to 2D+t. We demonstrate that the validation loss generally follows the true error in the learned terms and distil practical rules of thumb for selecting hyperparameters in the BINN architecture. By providing a structured workflow, practical guidelines, and suggested starting values for hyperparameter selection, this work lowers the barrier to BINN-based equation learning.

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/2610.02954 — 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 2026-10-05T23:01:38.656Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).