In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this context, new methods such as the virtual fields method and physics-informed neural networks have been developed as alternatives to the already established least-squares and finite element-based approaches. Moreover, model discovery problems are starting to emerge and can also be addressed in a parameter estimation framework. These developments call for a new unified perspective, which is able to cover both traditional parameter estimation methods and novel approaches in which the state variables or the model structure itself are inferred as well. Adopting concepts discussed in the inverse problems community, we distinguish between all-at-once and reduced approaches. With this general framework, we are able to structure a large portion of the literature on parameter estimation in computational mechanics - and we can identify combinations that have not yet been addressed, two of which are proposed in this paper. We also discuss statistical approaches to quantify the uncertainty related to the estimated parameters, and we propose a novel two-step procedure for identification of complex material models based on both frequentist and Bayesian principles. Finally, we illustrate and compare several of the aforementioned methods with mechanical benchmarks based on synthetic and real data.

翻译：在固体力学框架下，随着全场测量能力的进步和机器学习的再度兴起，从实验数据中推导材料参数的任务近年来重新成为研究热点。在此背景下，虚拟场方法、物理信息神经网络等新方法相继被提出，作为已有最小二乘法和有限元方法的替代方案。此外，模型发现问题开始涌现，也可在参数估计框架中加以解决。这些进展要求建立统一的新视角，既能涵盖传统参数估计方法，也能包含推断状态变量或模型结构本身的新颖方法。借鉴逆问题领域的概念，我们区分了全联立方法与简约方法。通过这一通用框架，我们能够系统梳理计算力学中参数估计领域的大部分文献，并识别尚未被探索的方法组合——其中两种将在本文中首次提出。我们还讨论了量化估计参数不确定性的统计学方法，并提出了基于频率学派与贝叶斯原理的复杂材料模型识别两步新流程。最后，我们通过基于合成数据与真实数据的力学基准测试，对上述多种方法进行了验证与对比分析。