Digital twinning offers a capability of effective real-time monitoring and control, which are vital for cost-intensive experimental facilities, particularly the ones where extreme conditions exist. Sparse experimental measurements collected by various diagnostic sensors are usually the only source of information available during the course of a physical experiment. Consequently, in order to enable monitoring and control of the experiment (digital twinning), the ability to perform inverse analysis, facilitating the full field solution reconstruction from the sparse experimental data in real time, is crucial. This paper shows for the first time that it is possible to directly solve inverse problems, such as solution reconstruction, where some or all boundary conditions (BCs) are unknown, by purely using a finite-element (FE) approach, without needing to employ any traditional inverse analysis techniques or any machine learning models, as is normally done in the field. This novel and efficient FE-based inverse analysis framework employs a conventional FE discretisation, splits the loading vector into two parts corresponding to the known and unknown BCs, and then defines a loss function based on that split. In spite of the loading vector split, the loss function preserves the element connectivity. This function is minimised using a gradient-based optimisation. Furthermore, this paper presents a novel modification of this approach, which allows it to generate a range of different solutions satisfying given requirements in a controlled manner. Controlled multiple solution generation in the context of inverse problems and their intrinsic ill-posedness is a novel notion, which has not been explored before. This is done in order to potentially introduce the capability of semi-autonomous system control with intermittent human intervention to the workflow.

翻译：数字孪生技术为实现高效实时监测与控制提供了可能，这对于成本高昂的实验设施（尤其是存在极端条件的设施）至关重要。各类诊断传感器采集的稀疏实验测量数据通常是物理实验过程中唯一可用的信息来源。因此，为实现实验监测与控制（数字孪生），执行反演分析以实时从稀疏实验数据重构全场解的能力极为关键。本文首次证明，无需采用该领域常用的传统反演分析技术或任何机器学习模型，仅通过有限元（FE）方法即可直接求解反问题（如解重构），即使部分或全部边界条件（BCs）未知。这种新颖高效的基于有限元的反演分析框架采用常规有限元离散化，将载荷向量拆分为已知与未知边界条件对应的两部分，并基于此拆分定义损失函数。尽管进行了载荷向量拆分，该损失函数仍保持单元连接性。通过基于梯度的优化方法对该函数进行最小化。此外，本文提出对该方法的新颖改进，使其能够以受控方式生成满足给定要求的一系列不同解。在反问题及其固有不适定性的背景下进行受控多解生成是一种全新概念，此前尚未被探索。此举旨在为工作流程引入间歇性人工干预的半自主系统控制能力。