Sep 2026· European Physical Journal B : Condensed Matter Physics· Vol 99· 0 citations· 60 references
TL;DR
A gradient-based adaptive spatially weighted PhyCRNet (GSW-PhyCRNet), where gradient information is utilized to guide adaptive spatial refinement, enabling the model to capture local spatial features and improve the fitting precision of physical constraints is proposed.
Convergence analysis verifies rapid error reduction and saturation with increasing resolution, establishing a practical adaptive framework for high-fidelity simulation of problems with localized sharp features in applied mechanics and computational physics.
A Physics-Informed Error Field Learning (PIEFL) framework for PINNs is proposed, which avoids continuous optimization of the entire solution space and focuses computational resources on correcting existing prediction errors.
Physics-Informed Neural Networks (PINNs) are a new method which, over the past few years, due to the development of the deep learning technology, has demonstrated significant potential in solving Partial Differential Equations (PDEs). Directly incorporating physical laws into the model training process does not only in...
Bo-Lin Liu· Theoretical and Natural Scie...· 0 citations
Physics-Informed Neural Networks (PINNs) are a hybrid modeling approach that integrates physical priors into neural networks. By encoding governing equations as soft constraint terms into the loss function, this method accomplishes organic integration of data-driven approaches with physical laws. PINNs demonstrate sign...
Yao Xiao, You-Min Tang, Yi Li et al.· Neural Networks· 0 citations
Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by incorporating governing physical laws into the training loss. For evolution equations, however, their conventional pointwise space--time representation does not explicitly encode temporal dependence, which can hinder accurate predic...
Xiao-Dong Feng, Zi-Yue Sun, Tao Tang et al.· 0 citations
The Physics-Informed Stochastic Configuration Machine is proposed, a novel backpropagation-free framework for both forward and inverse problems in differential equations that achieves high-fidelity predictive accuracy and robust parameter identification while accelerating the training process by orders of magnitude com...
Yueze Song, Zhong-Zhe Chen, Li-Hui Cen et al.· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
