使用基于 POD 的降阶建模进行水凝胶扩散-变形耦合的参数识别与不确定性传播
Parameter identification and uncertainty propagation of hydrogel coupled diffusion-deformation using POD-based reduced-order modeling
AI总结：
本文提出基于 POD 的水凝胶扩散-变形耦合降阶模型，通过溶胀基准与同轴打印案例验证，并结合全场优化实现材料参数高效识别及不确定性传播分析。
摘要：
本研究探索用于分析水凝胶随时间变化的扩散-变形行为的降阶建模。描述水凝胶瞬态行为的全阶模型由一个偏微分方程耦合系统构成，其中化学势与位移相互耦合。该系统以整体方式构建，并采用有限元法求解。我们采用 proper orthogonal decomposition（POD，本征正交分解）作为模型降阶方法。通过一个水凝胶溶胀基准问题和一个模拟同轴打印的案例研究，测试了降阶模型的性能。随后，我们将降阶模型嵌入优化循环，以利用全场数据高效识别该耦合问题的材料参数。最后，对材料参数的不确定性传播进行了研究。
英文摘要：
This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in which chemical potential and displacements are coupled. This system is formulated in a monolithic fashion and solved using the finite element method. We employ proper orthogonal decomposition as a model order reduction approach. The reduced-order model performance is tested through a benchmark problem on hydrogel swelling and a case study simulating co-axial printing. Then, we embed the reduced-order model into an optimization loop to efficiently identify the coupled problem's material parameters using full-field data. Finally, a study is conducted on the uncertainty propagation of the material parameter.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
