AI 中文总结
针对4D-STEM密集采样易损伤束敏样品的问题，提出嵌入弹性力学方程的PINN方法实现稀疏应变场重建，在低采样率下精度优于传统方法，还可提供不确定性估计，适配多材料体系。
AI 中文摘要
利用四维扫描透射电子显微镜（4D-STEM）进行定量应变测绘通常需要密集采样扫描，这可能会损伤对电子束敏感的样品。我们开发了一种用于稀疏4D-STEM应变重建的物理信息神经网络（PINN），该网络通过自动微分将弹性平衡和圣维南（Saint-Venant）相容性嵌入训练损失中。其架构结合了基于坐标的隐式表示、具有稳定二阶导数的正弦激活函数、冻结残差尺度归一化、指数物理权重递增策略以及基于残差的自适应配点法。我们将正弦激活残差网络应用于具有畴结构的PbGeSnSe₁.₅Te₁.₅的实验180×400像素应变图。在1%-75%的采样率（720-54000个探针位置）范围内，εₓₓ的R²值在10%采样率时达到0.80，在25%采样率时饱和至约0.86；仅用10%的探针位置即可恢复人字形应变带的形貌。在10%采样率下，与压缩感知相比，PINN将平均绝对误差降低了约26%，与高斯过程回归相比降低了22%。针对同等容量的纯数据驱动SIREN模型的消融实验表明，偏微分方程（PDE）先验在极端稀疏情况下提升了精度，并持续改善物理自洽性，但在数据充足时会给重建带来偏差。蒙特卡洛 dropout 和平均场变分推断提供了与重建误差相关的逐像素认知不确定性图。借助合适的本构模型，该框架可适配多种材料体系的应变测绘。
英文摘要
Quantitative strain mapping using four-dimensional scanning transmission electron microscopy (4D-STEM) typically requires densely sampled scans that can damage beam-sensitive specimens. We develop a physics-informed neural network (PINN) for sparse 4D-STEM strain reconstruction that embeds elastic equilibrium and Saint-Venant compatibility in the training loss through automatic differentiation. The architecture combines a coordinate-based implicit representation, sine activations with stable second derivatives, frozen residual-scale normalization, an exponential physics-weight ramp, and residual-based adaptive collocation. We apply a sine-activated residual network to an experimental $180\times400$-pixel strain map of domain-structured PbGeSnSe$_{1.5}$Te$_{1.5}$. Across $1$-$75%$ sampling ($720$-$54{,}000$ probe positions), $R^2$ for $\varepsilon_{xx}$ reaches $0.80$ at $10%$ sampling and saturates near $0.86$ by $25%$; the chevron strain-band morphology is recovered from $10%$ of probe positions. At $10%$ sampling, the PINN reduces mean absolute error by approximately $26%$ relative to compressed sensing and $22%$ relative to Gaussian-process regression. An ablation against an equal-capacity data-only SIREN shows that the PDE prior improves accuracy at extreme sparsity and consistently improves physical self-consistency, but biases the reconstruction when data are abundant. Monte Carlo dropout and mean-field variational inference provide per-pixel epistemic uncertainty maps correlated with reconstruction error. With an appropriate constitutive model, the framework is adaptable to strain mapping across diverse material systems.
Comments18 pages, 7 figures, 1 table, and Supplementary Material. Code and processed data are available at https://github.com/rmsreis/pinns-4dstem
