2026-10-14T00:17:06Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34046271 2026-10-01T14:24:25Z category_29779 item_type_1 month_year_10_2026

Schematic of the proposed dual-network physics-informed framework Gregorio Perez Bernal (22258905) Oscar Rincón Cardeño (22258780) Silvana Montoya-Noguera (22258901) Nicolas Guarin-Zapata (10712073) Applied mathematics not elsewhere classified scientific machine learning (SciML) Physics-Informed Neural Networks (PINNs) Kolmogorov-Arnold Networks(KAN) Inverse problems (Differential equations) Numerical solutions Unbounded domains <p dir="ltr">The coordinates $(x,y)$ are provided to two neural networks that simultaneously approximate the solution $\hat{u}$ and the unknown coefficient $\hat{k}$. We used uniform, Gaussian, and exponential sampling to distribute the PDE collocation points according to the computational domain. Automatic differentiation is used to evaluate the PDE residual, while solution and coefficient data losses are combined with the PDE residual to construct the composite loss. The two networks are jointly optimized by minimizing the resulting objective using Adam followed by L-BFGS</p> 2026-10-01T14:24:25Z Image Figure 10.6084/m9.figshare.34046271.v1 https://figshare.com/articles/figure/Schematic_of_the_proposed_dual-network_physics-informed_framework/34046271 CC BY 4.0