In this work, we have developed a variational Bayesian inference theory of elasticity, which is accomplished by using a mixed Variational Bayesian inference Finite Element Method (VBI-FEM) that can be used to solve the inverse deformation problems of continua. In the proposed variational Bayesian inference theory of continuum mechanics, the elastic strain energy is used as a prior in a Bayesian inference network, which can intelligently recover the detailed continuum deformation mappings with only given the information of the deformed and undeformed continuum body shapes without knowing the interior deformation and the precise actual boundary conditions, neither traction nor displacement boundary conditions, and the actual material constitutive relation. Moreover, we have implemented the related finite element formulation in a computational probabilistic mechanics framework. To numerically solve mixed variational problem, we developed an operator splitting or staggered algorithm that consists of the finite element (FE) step and the Bayesian learning (BL) step as an analogue of the well-known the Expectation-Maximization (EM) algorithm. By solving the mixed probabilistic Galerkin variational problem, we demonstrated that the proposed method is able to inversely predict continuum deformation mappings with strong discontinuity or fracture without knowing the external load conditions. The proposed method provides a robust machine intelligent solution for the long-sought-after inverse problem solution, which has been a major challenge in structure failure forensic pattern analysis in past several decades. The proposed method may become a promising artificial intelligence-based inverse method for solving general partial differential equations.

With the development of in-orbit satellite hardware technology, distributed model training and updating for in-orbit satellites has become a promising trend. However, performance significantly degrades due to heterogeneous data distribution and the lack of high-quality labeled data across satellites. To address these issues, we propose a distributed unsupervised representation learning method called Progressive Uniformity (DURL-PU) from a deep clustering perspective. DURL-PU explores instance-level, cluster-level, and structure-level representations to progressively enhance uniformity, thereby mitigating dimensional collapse caused by data heterogeneity. Specifically, we first perform instance-level contrastive learning to distinguish between positive and negative samples. Second, we introduce a cluster-level loss to improve within-cluster compactness and between-cluster dispersion while incorporating high-level semantic information. Finally, we propose a deep clustering-based structural loss to enhance the consistency of parameter distribution among different satellites. Extensive experiments under various heterogeneous data scenarios demonstrate the effectiveness of DURL-PU.

With the development of convolutional neural network (CNN), significant progress has been achieved in remote sensing image scene classification (RSISC). However, wide spatial range changes, complex scenes, as well as the high similarity between various classes and the significant difference in the same class, make it difficult to classify remote sensing images scenes. In this work, targetted at using finite remote sensing images to learn sufficient distinguishing features in a contrastive manner, we propose a novel multi-granularity and multi-scale progressive contrastive learning neural network (MMPC-Net). More specifically, we construct an end-to-end CNN model to mine discriminative features from multi-scale and multi-granularity representations. Afterwards, the discriminative knowledge between different features is summarized by introducing a progressive contrastive learning module, which can learn meaningful feature linking subtle changes in positive and negative pairs from massive samples. Experimental results over three widely-used benchmark datasets demonstrate that our methods can achieve comparative performance.