This study examines the influence of six collocation point sampling strategies—random uniform, uniform grid, Latin hypercube sampling, Sobol sequence, staggered triangular lattice, and a hybrid combined approach—on the performance of PINNs applied to the one-dimensional Burgers’ equation.
A robust and critical assessment of PINNs for solving the elastic wave equation in seismology is provided and it is demonstrated that this novel architecture enhances accuracy when applied to the acoustic wave equation, underlying the versatility of the network.
Experimental results confirm that the sampling strategy can effectively enhance the solution accuracy and provide reliable technical guidance for the optimization of sampling mechanisms in PINNs.
Xin-Yue Gao, Xiang-Hua Meng· The European Physical Journa...· 0 citations
The PMG framework is proposed as a data-free hybrid solver that does not rely on any pretraining and provides a unified mechanism to tightly couple the NN methods with classical iterative solvers, achieving an organic and iterative integration of the two paradigms.
Dai-Wei Dong, W. Suo, J. Kou et al.· Applied Mathematics and Mech...· 3 citations
The proposed ARH-PINNs can accurately resolve large-gradient fields such as shock waves, while effectively suppressing non-physical oscillations and retaining low numerical dissipation.
Ting-Jie Li, Su-Pei Zheng, Feng Hu et al.· The Physics of Fluids· 1 citation
A novel framework that combines Physics-Informed Neural Networks (PINNs) and Deep Galerkin Methods (DGM) is proposed to overcome difficulties in solving PDEs using AI, and it is shown that both techniques are highly accurate in the comparative analysis for a variety of parameter regimes.
Taimoor Iqbal, Shareen Shafique, Muhammad Asif· Journal of Machine Learning...· 0 citations
A regularized PINNs framework that incorporates Tikhonov regularization to solve terminal-state tracking optimal control constrained by parabolic partial differential equations is proposed, establishing a consistency result showing that PINNs minimizers nearly attain the continuous regularized objective under residual...
Q. Nguyen, T. Mai· 1 citation
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