https://doi.org/10.1140/epjp/s13360-025-07099-x
Regular Article
Leveraging enhanced physics-informed neural networks based on adaptive weight loss for solving inverse problems of nonlinear Sine-Gordon equation
Department of Applied Mathematics, Adama Science and Technology University, 1888, Adama, Oromia, Ethiopia
a
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Received:
17
July
2025
Accepted:
19
November
2025
Published online:
1
December
2025
The capacity of physics-informed neural networks (PINNs) to handle various nonlinear problems has attracted considerable attention recently. However, because PINNs rely on data points and physical constraint residuals to infer unknowns, they have a number of challenges and limitations, particularly when it comes to addressing complex inverse problems. The solution may be unstable or inaccurate when dealing with sparse or noisy data. In the current study, we propose adaptive weight loss PINNs (AWL-PINNs) to obtain the solution to inverse problems of a nonlinear space-time hyperbolic sine-Gordon equation. AWL-PINNs are an improved PINNs variant that is intended to increase training accuracy and efficiency. In addition, AWL-PINNs are utilized to balance contributions and enhance convergence by modifying the weights upon training according to the amount and rate of change of each loss term. The effectiveness and resilience of this approach are demonstrated through four computational examples. Different parameter identification and boundary control equations are considered among the types of inverse problems available. Two- and three-dimensional figures are displayed to show the dynamics and physical properties of both predicted solutions by the methods and accurate solutions. A comparison was made between AWL-PINN and standard PINN in terms of training and test losses and various error metrics. The tabular and graphical comparison results show that, compared to conventional PINNs, the proposed adaptive weight loss-based deep learning technique performs better in terms of accuracy, robustness, and computational efficiency for solving various inverse problems of nonlinear sine-Gordon equations. Furthermore, AWL-PINNs provide more dependable and repeatable results with less sensitivity to network initialization and data noise, according to statistical error evaluations. Hence, AWL-PINNs are an adaptable and remarkable machine learning tool to effectively handle similar inverse problems of nonlinear physical issues arising in various disciplines.
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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.
