AI 中文总结
该研究提出由分子动力学数据驱动的物理信息神经网络，结合自适应梯度归一化实现铁电体多尺度建模，可识别相场模型参数并重建极化等场，为跨尺度材料建模提供有效方法。
AI 中文摘要
在铁电体的多尺度建模中，将原子级模拟与连续尺度相场模型（PFM）结合仍是一项基础性挑战。关键难点在于在连续建模框架内忠实地捕捉离散原子级信息，同时准确表征介观尺度的材料行为。本文采用由分子动力学（MD）数据驱动的物理信息神经网络（PINN），其损失函数包含两项：一是拟合含畴壁系统的MD模拟所得离散空间极化分布的监督项，二是纳入稳态PFM偏微分方程（PDE）残差的物理项。为确保不同损失分量间训练稳定且平衡，采用自适应梯度归一化（GradNorm）动态调整任务权重。通过最小化总损失，模型不仅能在连续尺度重建极化场及相关应变、应力与能量分布，还能识别相场模型的关键物理参数，包括特征能量密度、特征长度因子、梯度能量各向异性因子及朗道多项式系数。将PINN预测的物理参数用于COMSOL Multiphysics中，在有限元框架内求解对应PDE，结果表明这些参数可准确复现铁电畴结构及相关材料响应，包括应力/应变分布与能量分布。该框架为建立原子级与连续级描述间的多尺度联系提供了有效方法，有望从多种材料的极化分布直接推断其潜在物理性质。
英文摘要
In multiscale modeling of ferroelectrics, combining atomistic simulation with continuum-scale phase-field models (PFM) remains a fundamental challenge. A key difficulty lies in faithfully capturing discrete atomic-level information within a continuum modeling framework, while accurately representing material behavior at the mesoscale. In this paper, a Physics-Informed Neural Network (PINN) driven by molecular dynamics (MD) data is used. The loss function of the network consists of a supervised term that fits the discrete spatial polarization distributions obtained from MD simulations of systems containing domain walls, and a physics-based term that incorporates the residuals of partial differential equations (PDEs) of steady-state PFM. To ensure stable and balanced training among the different loss components, adaptive gradient normalization (GradNorm) is used to dynamically adjust the task weights. By minimizing the total loss, the model not only reconstructs the polarization field along with the associated strain, stress, and energy landscape at the continuum scale, but also identifies critical physical parameters of the phase-field model, including the characteristic energy density, characteristic length factor, gradient energy anisotropy factor, and Landau polynomial coefficients. By using the PINN-predicted physical parameters in COMSOL Multiphysics to solve the corresponding PDEs within a finite element framework, we demonstrate that these parameters enable accurate reproduction of the ferroelectric domain structure and the associated material response, including stress/strain distributions and energy landscape. This framework provides an effective methodology for establishing multiscale connections between atomistic and continuum descriptions, and holds the potential to infer underlying physical properties directly from polarization distributions for a wide range of materials.
