PINNs-MPF：一种用于界面动力学多相场模拟的物理信息神经网络框架
PINNs-MPF: A Physics-Informed Neural Network Framework for Multi-Phase-Field Simulation of Interface Dynamics
AI总结：
本文提出PINNs-MPF框架，将物理信息神经网络与多相场方法结合，通过多网络协同、主神经网络交互和金字塔式训练策略，实现对界面动力学微观结构演化的高精度模拟。
摘要：
我们提出了物理信息神经网络（Physics-Informed Neural Networks）在多相场（MultiPhase-Field）模拟微观结构演化中的应用。研究表明，需要结合从PINNs文献中扩展和改编的优化技术，以及受MPF方法背景启发而引入的特定技术。数值求解通过使用全离散求解的多变量时间序列问题来实现。在每个区间内，空间、时间和相被分别处理，构成离散子域。实现了一种扩展的多网络概念，将模拟域细分为多个批次，每个批次与一个独立的神经网络相关联，该网络被训练用于预测解。为了确保不同相之间以及在时空-相子域中的高效交互，一个主神经网络（Master NN）处理多个网络之间的高效交互，以及不同方向上的学习迁移。执行了一组复杂性逐渐增加的系统性模拟，对MPF模拟的多个关键方面进行了基准测试，包括不同几何形状、界面动力学类型以及界面三叉节点的演化。采用了一种综合方法，通过自动和动态网格划分过程将注意力专门集中在界面区域，显著简化了超参数的调优，并作为使用机器学习解决MPF问题的关键基础。金字塔式训练方法作为双重影响方法被提出给PINNs社区：它有助于训练的初始化，并允许扩展的学习迁移。所提出的PINNs-MPF框架成功以高保真度重现了基准测试，与真值解相比，均方误差损失值范围为10$^{-4}$至10$^{-6}$。
英文摘要：
We present an application of Physics-Informed Neural Networks to handle MultiPhase-Field simulations of microstructure evolution. It has been showcased that a combination of optimization techniques extended and adapted from the PINNs literature, and the introduction of specific techniques inspired by the MPF Method background, is required. The numerical resolution is realized through a multi-variable time-series problem by using fully discrete resolution. Within each interval, space, time, and phases are treated separately, constituting discrete subdomains. An extended multi-networking concept is implemented to subdivide the simulation domain into multiple batches, with each batch associated with an independent Neural Network trained to predict the solution. To ensure efficient interaction across different phasesand in the spatio-temporal-phasic subdomain, a Master NN handles efficient interaction among the multiple networks, as well as the transfer of learning in different directions. A set of systematic simulations with increasing complexity was performed, that benchmarks various critical aspects of MPF simulations, including different geometries, types of interface dynamics and the evolution of an interfacial triple junction. A comprehensive approach is adopted to specifically focus the attention on the interfacial regions through an automatic and dynamic meshing process, significantly simplifying the tuning of hyper-parameters and serving as a fundamental key for addressing MPF problems using Machine Learning. The pyramidal training approach is proposed to the PINN community as a dual-impact method: it facilitates the initialization of training and allows an extended transfer of learning. The proposed PINNs-MPF framework successfully reproduces benchmark tests with high fidelity and Mean Squared Error loss values ranging from 10$^{-4}$ to 10$^{-6}$ compared to ground truth solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
