DDR-PINN: A Dynamic Domain–Gradient Reweighting Physics-Informed Neural Network
Lei S. Gulnar B. Yang C. Kunicina N. Grants R. Grunde U.
March 2026Multidisciplinary Digital Publishing Institute (MDPI)
Applied Sciences (Switzerland)
2026#16Issue 5
Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by embedding physical conditions as soft penalties into the loss function. However, the coexistence of multiple loss components often leads to gradient conflicts, degrading convergence and solution accuracy. To address this issue, we propose a dynamic domain–gradient loss reweighting PINN (DDR-PINN). The proposed method introduces a dual-residual reweighting mechanism based on gradient variations, where adaptive weights are derived from the L2 norm of the dot product between loss gradients and residuals. These weights are further normalized through a nonlinear hyperbolic tangent transformation, enabling dynamic and balanced reweighting of interior, initial, and boundary domain losses throughout training. Extensive numerical experiments on PDEs with both Dirichlet and Neumann boundary conditions demonstrate that the DDR-PINN consistently outperforms the standard PINN, APINN, and VI-PINN with the fewest trainable parameters.
loss reweighting , mathematical skills , partial differential equations , physics-informed neural networks , scientific machine learning
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Faculty of Information Technology and Artificial Intelligence, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Industrial Electronics, Electrical Engineering and Energy, Faculty of Computer Science, Information Technology and Energy, Riga Technical University, Riga, 1048, Latvia
Faculty of Information Technology and Artificial Intelligence
Institute of Industrial Electronics
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026