169936 20260306154908.0 doi 10.1016/j.cnsns.2026.109866 sideral 148441 ART-2026-148441 eng Martínez-Esteban, Andrés Physics-informed neural networks with dynamical boundary constraints 2026 Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way, the learned solution accounts for data (if available), the governing differential equations, or any other constraint known of the physical problem. However, they face serious issues, notably their tendency to converge on trivial or misleading solutions. The latter occurs when, although the loss function reaches low values, the model makes incorrect predictions. These difficulties become especially significant in differential equations involving multiscale behavior, such as those containing rapidly varying terms, as well as in problems whose solutions exhibit strong oscillatory behavior. To address these challenges, we introduce the Dynamical Boundary Constraint (DBC) algorithm, which imposes restrictions on the loss function based on prior training of the PINN. To demonstrate its applicability, we tested this approach on examples of different areas of physics. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E09-23R-QMAD info:eu-repo/grantAgreement/ES/MCIU/PID2023-148359NB-C21 info:eu-repo/grantAgreement/ES/MICIU/CEX2021-001144-S-20–10 info:eu-repo/grantAgreement/ES/MICIU/CEX2023-001286-S info:eu-repo/semantics/openAccess by-nc-nd https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Calvo-Barlés, Pablo (orcid)0000-0002-8371-9840 Martín-Moreno, Luis (orcid)0000-0001-9273-8165 Gutierrez Rodrigo, Sergio Universidad de Zaragoza (orcid)0000-0001-6575-168X 2002 647 Universidad de Zaragoza Dpto. Física Aplicada Área Óptica 158 (2026), 109866 [11 pp.] Commun. nonlinear sci. numer. simul. Communications in Nonlinear Science and Numerical Simulation 1007-5704 4098722 http://zaguan.unizar.es/record/169936/files/texto_completo.pdf Versión publicada 1989118 http://zaguan.unizar.es/record/169936/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:169936 articulos driver 2026-03-06-14:50:52 ARTICLE