标题： 解析与神经网络方法求解二维非线性瞬态热传导问题 显示英文标题

标题： Analytical and Neural Network Approaches for Solving Two-Dimensional Nonlinear Transient Heat Conduction

摘要： 准确预测二维区域中的非线性瞬态热场是多个工程领域中的重大挑战，其中传统解析和数值方法在处理强材料非线性和演变的多物理边界条件时，难以在物理保真度与计算效率之间取得平衡。 为解决这一挑战，我们提出了一种跨学科的新方法，将格林函数公式与自适应神经算子相结合，为多物理场热分析提供了一种新范式。 我们的方法结合了严格的解析推导与一种物理信息神经架构，该架构包含五个自适应隐藏层（每层64个神经元），将解作为物理约束，优化学习率以平衡收敛稳定性和计算速度。 广泛的验证表明，在处理快速热瞬态和强耦合非线性响应方面表现出卓越性能，这在保持与解析基准高度一致的同时显著提高了计算效率，适用于多种材料配置和边界条件。 显示英文摘要

摘要： Accurately predicting nonlinear transient thermal fields in two-dimensional domains is a significant challenge in various engineering fields, where conventional analytical and numerical methods struggle to balance physical fidelity with computational efficiency when dealing with strong material nonlinearities and evolving multiphysics boundary conditions. To address this challenge, we propose a novel cross-disciplinary approach integrating Green's function formulations with adaptive neural operators, enabling a new paradigm for multiphysics thermal analysis. Our methodology combines rigorous analytical derivations with a physics-informed neural architecture consisting of five adaptive hidden layers (64 neurons per layer) that incorporates solutions as physical constraints, optimizing learning rates to balance convergence stability and computational speed. Extensive validation demonstrates superior performance in handling rapid thermal transients and strongly coupled nonlinear responses, which significantly improves computational efficiency while maintaining high agreement with analytical benchmarks across a range of material configurations and boundary conditions.