The calibration of constitutive models from full-field data has recently gained increasing interest due to improvements in full-field measurement capabilities. In addition to the experimental characterization of novel materials, continuous structural health monitoring is another application that is of great interest. However, monitoring is usually associated with severe time constraints, difficult to meet with standard numerical approaches. Therefore, parametric physics-informed neural networks (PINNs) for constitutive model calibration from full-field displacement data are investigated. In an offline stage, a parametric PINN can be trained to learn a parameterized solution of the underlying partial differential equation. In the subsequent online stage, the parametric PINN then acts as a surrogate for the parameters-to-state map in calibration. We test the proposed approach for the deterministic least-squares calibration of a linear elastic as well as a hyperelastic constitutive model from noisy synthetic displacement data. We further carry out Markov chain Monte Carlo-based Bayesian inference to quantify the uncertainty. A proper statistical evaluation of the results underlines the high accuracy of the deterministic calibration and that the estimated uncertainty is valid. Finally, we consider experimental data and show that the results are in good agreement with a Finite Element Method-based calibration. Due to the fast evaluation of PINNs, calibration can be performed in near real-time. This advantage is particularly evident in many-query applications such as Markov chain Monte Carlo-based Bayesian inference.

翻译：近年来，随着全场测量技术的进步，基于全场数据的本构模型标定研究日益受到关注。除新型材料的实验表征外，连续结构健康监测是另一个备受关注的应用领域。然而，监测任务通常面临严格的时间约束，传统数值方法难以满足实时性要求。为此，本研究探讨利用参数化物理信息神经网络（PINNs）从全场位移数据中实现本构模型标定。在离线阶段，通过训练参数化PINN学习底层偏微分方程的参数化解；在后续在线阶段，该网络将作为参数-状态映射的代理模型参与标定过程。我们在线弹性与超弹性本构模型的确定性最小二乘标定中验证了所提方法，使用含噪声合成位移数据进行测试。进一步通过马尔可夫链蒙特卡洛贝叶斯推断实现不确定性量化。统计评估结果表明：确定性标定具有高精度，且估计的不确定性范围有效。最后，通过实验数据验证，显示该方法与基于有限元法的标定结果高度吻合。由于PINNs的快速求解特性，标定过程可实现近实时执行，这一优势在马尔可夫链蒙特卡洛贝叶斯推断等多查询应用中尤为显著。