2026· International Conference on Conceptual Structures· pp. 567-574· 0 citations· 12 references
Computer Science
TL;DR
Collocation-based Robust Variational PINNs (CRVPINN) aim to regain the efficiency of PINNs while retaining robustness by applying the RVPINN framework to variational formulations based on discrete grids and finite difference approximations.
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.
Ruslan Krasnozhonov, M. Nurtas, Zh. M. Kadirbayeva et al.· AI@DTESI· 0 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
Experiments show that FC-VPINN achieves approximately one-order-of-magnitude lower prediction errors than the traditional PINN and reduces memory usage to 40% of that required by the baseline, demonstrating improved accuracy and computational efficiency in multidimensional problems.
Wenjie Zhang, Yu-Bo Li, Wei-Dong Cui et al.· Chinese Physics B· 0 citations
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.
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
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
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