发表机构
Korea Institute of Energy Technology（韩国能源技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对Allen--Cahn方程无法同时辨识自由能势与界面尺度的问题，提出表面张力校准两步法，利用Bernstein正系数约束与岭正则化，在80个噪声记录上将力误差从8.70%降至5.66%，并实现结构容许且物理标定的势恢复。
AI 中文摘要
由Allen--Cahn方程控制的相场轨迹决定了有效力$G=F'/\eps^2$，但无法分别确定自由能势$F$和界面尺度$\eps$。我们提出了表面张力校准的Allen--Cahn辨识（STAC），这是一种两步方法，利用独立提供的表面张力来解决这一模糊性。首先，时空弱矩产生一个线性逆问题，无需对测量场进行微分。具有正系数的Bernstein表示强制两个稳定的纯相和一个单一的中心能量最大值。其次，表面张力通过代数方式确定剩余的尺度。我们证明了正演模型的尺度等价性、该类内校准对的唯一性，以及在势在纯相处消失时仍然有效的有限扰动界。使用解析合成相场的实验分离了结构约束、岭正则化和本构逼近误差的影响。在80个共享的含噪记录中，无约束的五次回归产生了六个具有错误阱结构的势。正性与岭正则化相结合消除了这些违规，并将平均力误差从8.70%降至5.66%。然而，在某些测试中，低阶模型更为准确，并且正Bernstein族之外的一个容许法则显示了约束如何引入逼近偏差。因此，STAC恢复了一个结构上容许、物理上标定的势，同时明确了哪些信息来自观测动力学，哪些来自独立的表面张力数据。
英文摘要
Phase-field trajectories governed by the Allen--Cahn equation determine the effective force $G=F'/\eps^2$, but not the free-energy potential $F$ and interfacial scale $\eps$ separately. We introduce surface-tension-calibrated Allen--Cahn identification (STAC), a two-step method that resolves this ambiguity using an independently supplied surface tension. First, space--time weak moments produce a linear inverse problem without differentiating the measured field. A Bernstein representation with positive coefficients enforces two stable pure phases and a single central energy maximum. Second, the surface tension fixes the remaining scale algebraically. We prove scale equivalence of the forward model, uniqueness of the calibrated pair within this class, and finite perturbation bounds that remain valid when the potential vanishes at the pure phases. Experiments with resolved synthetic phase fields separate the effects of the structural constraint, ridge regularization, and constitutive approximation error. Across 80 shared noisy records, unconstrained degree-five regression produces six potentials with an incorrect well structure. Positivity combined with ridge regularization eliminates these violations and reduces the mean force error from 8.70\% to 5.66\%. Lower-degree models are nevertheless more accurate in some tests, and an admissible law outside the positive Bernstein family shows how the constraint can introduce approximation bias. STAC thus recovers a structurally admissible, physically scaled potential while making explicit which information comes from the observed dynamics and which comes from the independent surface-tension datum.
