发表机构
Department of Energy Engineering, Korea Institute of Energy Technology（韩国能源技术研究院能源工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对含噪Allen-Cahn图像推断本构力问题，提出观测感知矩方程与SCCT模型，校正噪声偏差，提升力推断精度，并成功预测未见演化。
AI 中文摘要
从图像中推断Allen-Cahn本构力不仅需要精确的优化器：非线性观测噪声会改变力特征的均值，共享噪声将仪器与响应耦合，而借用其他求解器的时间平衡即使在干净数据上也可能存在偏差。我们开发了观测感知、噪声调整的矩方程，在反演之前解决这些影响。表面张力校准的本构变换器（SCCT）将所得矩与正Bernstein逆变换耦合，并能从图像和矩中自适应其先验和精度。条件稳定性界将矩残差与先验误差分离。合成测试表明，校正估计方程比增加正则化器灵活性更重要；学习自适应的收益较小且依赖于训练对比。从平面电影推断的力可预测未见过的平面和三维演化。环-笼破裂展示了为什么扩散界面精度能区分力，即使它们的拓扑预测一致，而外部表面张力单独设定能量尺度。
英文摘要
Inferring an Allen-Cahn constitutive force from images requires more than an accurate optimizer: nonlinear observation noise alters the mean of force features, shared noise couples instruments to the response, and a temporal balance borrowed from another solver can remain biased even on clean data. We develop observation-aware, noise-adjusted moment equations that address these effects before inversion. The surface-tension-calibrated constitutive transformer (SCCT) couples the resulting moments to a positive Bernstein inverse and can adapt its prior and precision from images and moments. A conditional stability bound separates moment residuals from prior error. Synthetic tests show that correcting the estimating equation matters more than increasing regularizer flexibility; the benefit of learned adaptation is smaller and depends on the training comparison. Forces inferred from planar movies predict unseen planar and three-dimensional evolutions. A ring-cage breakup shows why diffuse-interface accuracy distinguishes forces even when their topological predictions agree, while external surface tension sets the energy scale separately.
Comments30 pages, 18 figures
