.png){kind=icon}
返回
Antiderivative-enhanced adaptive sampling algorithm for physics-informed neural networks
.png){kind=icon}
PRE
AI
DOI：10.1088/1402-4896/ae30b5.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Physics-informed neural networks (PINNs) effectively integrate physical equation constraints into the model to simultaneously learn data distributions and underlying physical laws. However, conventional uniform sampling is computationally expensive and inefficient for complex systems. The residual-based adaptive refinement distribution (RARD) algorithm, proposed by Wang et al, improves sampling but relies heavily on residual estimation, neglecting higher-order derivatives and leading to potential suboptimal sampling distributions. To address these issues, this study proposes the Residual-based Adaptive Antiderivative Approximation (RA-ADAF) approach. Within a fully connected neural network (FCNN) framework, RA-ADAF introduces antiderivative approximation layers (ADAF) with integral structure modeling capability, enhancing the representation of both the target function and its derivatives. Unlike the RARD strategy that solely relies on residual estimation for adaptive sampling, RA-ADAF combines residual-driven adaptive sampling with derivative-informed structural modeling. This dual mechanism improves model fitting in error-concentrated regions and enhances the representation of higher-order derivative behavior. The effectiveness of the RA-ADAF method is validated through a series of numerical experiments, including comparisons on the Burgers equation, Allen–Cahn equation, wave equation and 2D Poisson equation, as well as ablation studies. Experimental results demonstrate that RA-ADAF consistently achieves lower relative L2 error compared to the RARD method across multiple test cases. Moreover, it exhibits faster error convergence and more stable training behavior, providing a more reliable strategy for solving partial differential equations (PDEs) involving complex physical phenomena.
期刊
IF:
2.6
论文数:
4.3K
被引数:
2.5W
机构
引用论文
DMIS: Dynamic Mesh-Based Importance Sampling for Training Physics-Informed Neural NetworksDMIS: 基于动态网格的重要性采样方法用于训练物理信息神经网络
OAAI
OAAI分享收藏Gradient-enhanced physics-informed neural networks for forward and inverse PDE用于正向和反向PDE的梯度增强物理通知神经网络
OAAI
OAAI分享收藏Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations物理信息神经网络: 一种用于解决涉及非线性偏微分方程的正反问题的深度学习框架OAAI
OAAI分享收藏A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks物理信息神经网络的非自适应和基于残差的自适应采样的综合研究OAAI
OAAI分享收藏Orthogonal grid physics-informed neural networks: A neural network-based simulation tool for advection-diffusion-reaction problems.png)
PHYSICS OF FLUIDS
PHYSICS OF FLUIDSIF4.3
PREAI
分享收藏A physics-informed neural network technique based on a modified loss function for computational 2D and 3D solid mechanics基于改进的损失函数的物理信息神经网络技术，用于计算2D和3D固体力学
PREAI
分享收藏TCAS-PINN: Physics-informed neural networks with a novel temporal causality-based adaptive sampling methodTCAS-PINN：一种结合基于新型时序因果关系的自适应采样方法的物理信息神经网络
PREAI
分享收藏Efficient training of physics-informed neural networks via importance sampling通过重要性采样有效训练物理信息神经网络OAAI
OAAI分享收藏
查看更多内容