Identifying constitutive parameters in engineering and biological materials, particularly those with intricate geometries and mechanical behaviors, remains a longstanding challenge. The recent advent of Physics-Informed Neural Networks (PINNs) offers promising solutions, but current frameworks are often limited to basic constitutive laws and encounter practical constraints when combined with experimental data. In this paper, we introduce a robust PINN-based framework designed to identify material parameters for soft materials, specifically those exhibiting complex constitutive behaviors, under large deformation in plane stress conditions. Distinctively, our model emphasizes training PINNs with multi-modal synthetic experimental datasets consisting of full-field deformation and loading history, ensuring algorithm robustness even with noisy data. Our results reveal that the PINNs framework can accurately identify constitutive parameters of the incompressible Arruda-Boyce model for samples with intricate geometries, maintaining an error below 5%, even with an experimental noise level of 5%. We believe our framework provides a robust modulus identification approach for complex solids, especially for those with geometrical and constitutive complexity.
Medical image segmentation in X-ray images is beneficial for computer-aided diagnosis and lesion localization. Existing methods mainly fall into a centralized learning paradigm, which is inapplicable in the practical medical scenario that only has access to distributed data islands. Federated Learning has the potential to offer a distributed solution but struggles with heavy training instability due to client-wise domain heterogeneity (including distribution diversity and class imbalance). In this paper, we propose a novel Federated Client-tailored Adapter (FCA) framework for medical image segmentation, which achieves stable and client-tailored adaptive segmentation without sharing sensitive local data. Specifically, the federated adapter stirs universal knowledge in off-the-shelf medical foundation models to stabilize the federated training process. In addition, we develop two client-tailored federated updating strategies that adaptively decompose the adapter into common and individual components, then globally and independently update the parameter groups associated with common client-invariant and individual client-specific units, respectively. They further stabilize the heterogeneous federated learning process and realize optimal client-tailored instead of sub-optimal global-compromised segmentation models. Extensive experiments on three large-scale datasets demonstrate the effectiveness and superiority of the proposed FCA framework for federated medical segmentation.