AI 中文总结
研究从小冲孔试验多模态测量估计材料本构参数问题，提出将高斯过程代理与条件流匹配相结合的摊销无似然框架，避免手工似然和重复采样，通过实验证明该方法能有效收缩后验，建立了强大的无似然推断框架。
AI 中文摘要
从多模态力学测试数据对材料本构参数进行贝叶斯校准，常因需指定跨维度、噪声结构和物理单位不同的测量模态的联合似然而受限。由此产生的后验往往宽泛或强相关，导致标准马尔可夫链蒙特卡罗（MCMC）采样器混合不佳。本文提出一种摊销的、无似然框架，将高斯过程（GP）代理与条件流匹配（CFM）相结合，直接从合成多模态参数 - 观测对学习本构参数的条件后验，避免手工似然和重复MCMC采样。训练后，GP - CFM模型以可忽略的成本为每个新样本生成后验样本。通过从小冲孔试验（SPT）中力 - 位移（$F$ - $D$）曲线早期部分和基于数字图像相关（DIC）的位移场估计杨氏模量和屈服强度值，证明了该新方法的实用性。仅$F$ - $D$数据产生宽泛后验，与全局响应中有限的参数辨别一致。添加DIC测量的位移场使后验收缩并向独立测量的拉伸参考值移动。这项工作通过SPT - DIC集成建立了一个用于从多模态数据推断材料本构参数的强大无似然框架。
英文摘要
Bayesian calibration of material constitutive parameters from multimodal mechanical test data is often limited by the need to specify a joint likelihood across measurement modalities that differ in dimensionality, noise structure, and physical units. The resulting posteriors are often broad or strongly correlated, causing standard Markov Chain Monte Carlo (MCMC) samplers to mix poorly. Here, we present an amortized, likelihood-free framework that combines Gaussian process (GP) surrogates with Conditional Flow Matching (CFM) to learn conditional posteriors over constitutive parameters directly from synthetic multimodal parameter--observation pairs, avoiding hand-crafted likelihoods and repeated MCMC sampling. Once trained, the GP--CFM model generates posterior samples for each new specimen at negligible cost. The utility of this novel approach is demonstrated in this paper by estimating the values of Young's modulus and yield strength from the early portion of the force--displacement ($F$--$D$) curve and a Digital Image Correlation (DIC)-based displacement field measured in a Small Punch Test (SPT). It is observed that the $F$--$D$ data alone produce broad posteriors, consistent with limited parameter discrimination in the global response. Adding the DIC-measured displacement field was seen to contract the posteriors and shift them towards the independently measured tensile reference values. This work establishes a robust likelihood-free framework for the inference of material constitutive parameters from multimodal data, demonstrated through SPT--DIC integration.
