铀矿地质2025，Vol.41Issue(6)：1126-1137,12.DOI:10.3969/j.issn.1000-0658.2025.41.078
基于Crank-Nicolson离散化的物理信息神经网络在含铀流体迁移模拟中的应用
Application of Physics-Informed Neural Networks with Crank-Nicolson Discretization in the Simulation of Uranium-bearing Fluid Migration
摘要
Abstract
In the process of uranium mineralization,the simulation of uranium-bearing fluid migration is of great significance for resource development and environmental assessment.Although traditional numerical methods have made some progress in simulating uranium-bearing fluid migration,but have limitations in handling highly heterogeneous media and nonlinear problems.As an emerging computational approach,Physics-Informed Neural Networks(PINN)exhibit potential in addressing strongly nonlinear problems through mesh-free solutions and the embedding of physical equations.However,when solving nonlinear partial differential equations in time-stepping processes,PINN still faces challenges in accuracy and computational efficiency.To address this issue,this paper proposes an innovative solution method that integrates the Crank-Nicolson discretization with PINN,significantly enhancing the numerical stability and solution accuracy during time advancement.Using the one-dimensional Burgers´ equation as a model,we made a simulation of uranium-bearing fluid migration in groundwater environments.The results demonstrate that the proposed method achieves high-accuracy solutions across the computational domain,regardless of whether uniform or non-uniform time steps are employed.关键词
物理信息神经网络/含铀流体迁移/非线性偏微分方程/Burgers方程/Crank-NicolsonKey words
Physics-Informed Neural Networks(PINN)/uranium-bearing fluid migration/nonlinear partial differential equations/Burgers equation/Crank-Nicolson method引用本文复制引用
彭智婷,刘龙成,张喆安,牛思源,白云龙..基于Crank-Nicolson离散化的物理信息神经网络在含铀流体迁移模拟中的应用[J].铀矿地质,2025,41(6):1126-1137,12.基金项目
中核集团基础研究项目"基于人工智能算法的含水层岩性结构及地下水流场的识别及演化研究"(编号:CNNC-JCYC-202429)资助. （编号:CNNC-JCYC-202429）
