Adaptive Hard-Soft Physics-Informed Neural Networks for Robust Boundary-Constrained PDE Solving
Physics-informed neural networks (PINNs) provide an effective way to solve partial differential equations (PDEs) by embedding physical principles into the learning process. However, the conventional PINN formulation, in which all constraints are imposed as soft penalty terms within a composite loss, often exhibits slow convergence, sensitivity to loss weight scaling, and inaccurate boundary enforcement due to poor conditioning of the optimization landscape. To address these limitations, this study proposes a unified hard--soft physics--informed neural network (HSPINN) with adaptive loss weighting. In this framework, Dirichlet and periodic boundary conditions are enforced exactly by constr...
| Authors | Duc Tien Nguyen, Trinh Minh Tuan, Nguyen Duc Manh et al. |
|---|---|
| Primary category | cs.LG |
| Published | 22 June 2026 |
| Last updated at source | 22 June 2026 |
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