Manifold fitting with CycleGAN.

Manifold fitting, which offers substantial potential for efficient and accurate modeling, poses a critical challenge in nonlinear data analysis. This study presents an approach that employs neural networks to fit the latent manifold. Leveraging the generative adversarial framework, this method learns smooth mappings between low-dimensional latent space and high-dimensional ambient space, echoing the Riemannian exponential and logarithmic maps. The well-trained neural networks provide estimations for the latent manifold, facilitate data projection onto the manifold, and even generate data points that reside directly within the manifold. Through an extensive series of simulation studies and real data experiments, we demonstrate the effectiveness and accuracy of our approach in capturing the inherent structure of the underlying manifold within the ambient space data. Notably, our method exceeds the computational efficiency limitations of previous approaches and offers control over the dimensionality and smoothness of the resulting manifold. This advancement holds significant potential in the fields of statistics and computer science. The seamless integration of powerful neural network architectures with generative adversarial techniques unlocks possibilities for manifold fitting, thereby enhancing data analysis. The implications of our findings span diverse applications, from dimensionality reduction and data visualization to generating authentic data. Collectively, our research paves the way for future advancements in nonlinear data analysis and offers a beacon for subsequent scholarly pursuits.

A minimally designed soft crawling robot for robust locomotion in unstructured pipes.

Soft robots have attracted increasing attention due to their excellent versatility and broad applications. In this article, we present a minimally designed soft crawling robot (SCR) capable of robust locomotion in unstructured pipes with various geometric/material properties and surface topology. In particular, the SCR can squeeze through narrow pipes smaller than its cross section and propel robustly in spiked pipes. The gait pattern and locomotion mechanism of this robot are experimentally investigated and analysed by the finite element analysis, revealing that the resultant forward frictional force is generated due to the asymmetric mechanical properties along the length direction of the robot. The proposed simple yet working SCR could inspire novel designs and applications of soft robots in unstructured narrow canals such as large intestines or industrial pipelines.