AI 中文总结
针对移动接触线问题，提出MCL-PINNs相场神经求解器，基于离散时间公式，结合多网络时间推进等关键技术，经三个数值例子验证，相比标准PINNs显著提高预测精度和鲁棒性，能解决复杂界面演化和接触线动力学问题。
AI 中文摘要
基于Cahn-Hilliard方程并结合动态边界条件的相场模型为移动接触线（MCL）问题提供了一个热力学一致的框架。尽管物理信息神经网络（PINNs）为求解偏微分方程提供了一种无网格方法，但由于长期误差积累、尖锐界面轮廓、局部接触线动力学和复杂接触角演化，其直接应用于MCL问题仍然具有挑战性。在这项工作中，我们提出了MCL-PINNs，一种专门为具有动态边界条件的MCL问题设计的相场神经求解器。该方法基于离散时间公式构建，并结合了几种关键技术，包括多网络时间推进方案、对神经网络输出的松弛分布约束、对急剧变化的解特征的可变缩放、自适应损失加权、带有界面提取的自适应配置采样，以及在适用时通过神经网络输入保持对称性。这些技术提高了神经求解器解决尖锐界面轮廓和接触线运动的能力。所提出的方法通过三个数值例子进行了验证，包括液滴聚结、剪切诱导的液滴变形和非均匀通道中的动态润湿。数值结果表明，与标准PINNs公式相比，MCL-PINNs显著提高了预测精度和鲁棒性，能够可靠地解决复杂的界面演化和移动接触线动力学问题。
英文摘要
Phase-field models based on the Cahn--Hilliard equation coupled with dynamic boundary conditions provide a thermodynamically consistent framework for moving contact line (MCL) problems. Although physics-informed neural networks (PINNs) offer a mesh-free approach for solving partial differential equations, their direct application to MCL problems remains challenging due to long-time error accumulation, sharp interfacial profiles, localized contact line dynamics, and complex contact angle evolution. In this work, we propose MCL-PINNs, a specialized phase-field neural solver designed for MCL problems with dynamic boundary conditions. The method is built on a discrete-time formulation and incorporates several key techniques, including a multi-network time-marching scheme, a relaxed distribution constraint on the neural network outputs, variable scaling for sharply varying solution features, adaptive loss weighting, adaptive collocation sampling with interface extraction, and, when applicable, symmetry preservation through neural network inputs. These techniques improve the capability of the neural solver in resolving sharp interfacial profiles and contact line motion. The proposed method is validated through three numerical examples involving droplet coalescence, shear-induced droplet deformation, and dynamic wetting in a heterogeneous channel. The numerical results show that MCL-PINNs significantly improve prediction accuracy and robustness compared with standard PINNs formulations, enabling reliable resolution of complex interfacial evolution and moving contact line dynamics.
