cs.AI updates on arXiv.org 10月01日
物理信息神经网络与多片等几何分析结合求解偏微分方程
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本文提出一种将物理信息神经网络与多片等几何分析相结合的计算框架,用于解决复杂计算机辅助设计几何形状上的偏微分方程。该方法利用局部神经网络在等几何分析的参考域上运行,并通过定制输出层和专用界面神经网络确保解的一致性。以两个实际案例验证了方法的有效性。

arXiv:2509.25450v1 Announce Type: cross Abstract: This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes patch-local neural networks that operate on the reference domain of isogeometric analysis. A custom output layer enables the strong imposition of Dirichlet boundary conditions. Solution conformity across interfaces between non-uniform rational B-spline patches is enforced using dedicated interface neural networks. Training is performed using the variational framework by minimizing the energy functional derived after the weak form of the partial differential equation. The effectiveness of the suggested method is demonstrated on two highly non-trivial and practically relevant use-cases, namely, a 2D magnetostatics model of a quadrupole magnet and a 3D nonlinear solid and contact mechanics model of a mechanical holder. The results show excellent agreement to reference solutions obtained with high-fidelity finite element solvers, thus highlighting the potential of the suggested neural solver to tackle complex engineering problems given the corresponding computer-aided design models.

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物理信息神经网络 等几何分析 偏微分方程 计算机辅助设计 神经网络求解
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