https://doi.org/10.1140/epjp/s13360-025-06644-y
Regular Article
An enhanced deep neural network with global adaptive weighted gradient for solving hyperbolic partial differential equations
1
School of Mathematical Sciences, University of Electronic Science and Technology of China, 611731, Chengdu, Sichuan, China
2
College of Mathematics and System Sciences, Xinjiang University, 830046, Urumqi, China
Received:
2
May
2025
Accepted:
9
July
2025
Published online:
27
July
2025
Physics-informed neural networks (PINNs) are a robust deep learning framework for solving partial differential equations (PDEs). However, solving hyperbolic PDEs often results in conflicting interactions among loss function components. To address this problem, we propose an enhanced deep neural network with global adaptive weights to improve classical PINNs. This enhanced architecture boosts expressiveness for better function approximation, while adaptive weights dynamically balance loss components to reduce convergence oscillations. Numerical experiments show that, despite increased loss function complexity, our approach outperforms classical PINNs in training efficiency, computational accuracy, and generalization.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
