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000169936 005__ 20260306154908.0
000169936 0247_ $$2doi$$a10.1016/j.cnsns.2026.109866
000169936 0248_ $$2sideral$$a148441
000169936 037__ $$aART-2026-148441
000169936 041__ $$aeng
000169936 100__ $$aMartínez-Esteban, Andrés
000169936 245__ $$aPhysics-informed neural networks with dynamical boundary constraints
000169936 260__ $$c2026
000169936 5060_ $$aAccess copy available to the general public$$fUnrestricted
000169936 5203_ $$aPhysics-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.
000169936 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E09-23R-QMAD$$9info:eu-repo/grantAgreement/ES/MCIU/PID2023-148359NB-C21$$9info:eu-repo/grantAgreement/ES/MICIU/CEX2021-001144-S-20–10$$9info:eu-repo/grantAgreement/ES/MICIU/CEX2023-001286-S
000169936 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
000169936 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000169936 700__ $$0(orcid)0000-0002-8371-9840$$aCalvo-Barlés, Pablo
000169936 700__ $$0(orcid)0000-0001-9273-8165$$aMartín-Moreno, Luis
000169936 700__ $$0(orcid)0000-0001-6575-168X$$aGutierrez Rodrigo, Sergio$$uUniversidad de Zaragoza
000169936 7102_ $$12002$$2647$$aUniversidad de Zaragoza$$bDpto. Física Aplicada$$cÁrea Óptica
000169936 773__ $$g158 (2026), 109866 [11 pp.]$$pCommun. nonlinear sci. numer. simul.$$tCommunications in Nonlinear Science and Numerical Simulation$$x1007-5704
000169936 8564_ $$s4098722$$uhttps://zaguan.unizar.es/record/169936/files/texto_completo.pdf$$yVersión publicada
000169936 8564_ $$s1989118$$uhttps://zaguan.unizar.es/record/169936/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000169936 909CO $$ooai:zaguan.unizar.es:169936$$particulos$$pdriver
000169936 951__ $$a2026-03-06-14:50:52
000169936 980__ $$aARTICLE