Towards Efficient and Effective Deep Clustering with Dynamic Grouping and Prototype Aggregation

Previous contrastive deep clustering methods mostly focus on instance-level information while overlooking the member relationship within groups/clusters, which may significantly undermine their representation learning and clustering capability. Recently, some group-contrastive methods have been developed, which, however, typically rely on the samples of the entire dataset to obtain pseudo labels and lack the ability to efficiently update the group assignments in a batch-wise manner. To tackle these critical issues, we present a novel end-to-end deep clustering framework with dynamic grouping and prototype aggregation, termed as DigPro. Specifically, the proposed dynamic grouping extends contrastive learning from instance-level to group-level, which is effective and efficient for timely updating groups. Meanwhile, we perform contrastive learning on prototypes in a spherical feature space, termed as prototype aggregation, which aims to maximize the inter-cluster distance. Notably, with an expectation-maximization framework, DigPro simultaneously takes advantage of compact intra-cluster connections, well-separated clusters, and efficient group updating during the self-supervised training. Extensive experiments on six image benchmarks demonstrate the superior performance of our approach over the state-of-the-art. Code is available at https://github.com/Regan-Zhang/DigPro

Modelling the Self-similarity in Complex Networks Based on Coulomb's Law

Recently, self-similarity of complex networks have attracted much attention. Fractal dimension of complex network is an open issue. Hub repulsion plays an important role in fractal topologies. This paper models the repulsion among the nodes in the complex networks in calculation of the fractal dimension of the networks. The Coulomb's law is adopted to represent the repulse between two nodes of the network quantitatively. A new method to calculate the fractal dimension of complex networks is proposed. The Sierpinski triangle network and some real complex networks are investigated. The results are illustrated to show that the new model of self-similarity of complex networks is reasonable and efficient.Comment: 25 pages, 11 figure

Multi-fractal analysis of weighted networks

In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal dimension to study complex networks. In this case, multifractal analysis of complex networks are concerned. However, multifractal dimension of weighted networks are less involved. In this paper, multifractal dimension of weighted networks is proposed based on box-covering algorithm for fractal dimension of weighted networks (BCANw). The proposed method is applied to calculate the fractal dimensions of some real networks. Our numerical results indicate that the proposed method is efficient for analysis fractal property of weighted networks

Physically Interpretable Feature Learning and Inverse Design of Supercritical Airfoils

Machine-learning models have demonstrated a great ability to learn complex patterns and make predictions. In high-dimensional nonlinear problems of fluid dynamics, data representation often greatly affects the performance and interpretability of machine learning algorithms. With the increasing application of machine learning in fluid dynamics studies, the need for physically explainable models continues to grow. This paper proposes a feature learning algorithm based on variational autoencoders, which is able to assign physical features to some latent variables of the variational autoencoder. In addition, it is theoretically proved that the remaining latent variables are independent of the physical features. The proposed algorithm is trained to include shock wave features in its latent variables for the reconstruction of supercritical pressure distributions. The reconstruction accuracy and physical interpretability are also compared with those of other variational autoencoders. Then, the proposed algorithm is used for the inverse design of supercritical airfoils, which enables the generation of airfoil geometries based on physical features rather than the complete pressure distributions. It also demonstrates the ability to manipulate certain pressure distribution features of the airfoil without changing the others

Gene regulatory network and epigenetic reprogramming of pig primordial germ cells

Primordial germ cells (PGC) are the precursors of the gametes. The mechanisms of PGC induction, specification and development are very well characterized in rodents, however recent investigations have demonstrated that the mechanisms of germ cell development differ significantly between mice and humans. Since the knowledge of PGC development in non-rodents is very limited, and early human embryos cannot be accessed it is important to establish a new model for PGC development with relevance to humans. In this thesis, I use pig embryo as a model for investigating PGC development in non-rodent mammals. The expression profile of key transcription factors, epigenetic reprograming and the role of signalling pathways were investigated during specification and development of pig PGCs. The key findings are: A- Specification of porcine PGC occurs after the onset of gastrulation, requiring BMP4 signalling. B- WNT signalling is required for the generation of precursors competent for germline commitment; however it is downregulated after PGCs are specified. WNT downregulation could be modulated by SOX17, the earliest gene expressed in pig PGCs. C- Epigenetic reprogramming of DNA and histone marks starts in pre-migratory porcine PGC. Furthermore, chromatin dynamics in pig gonadal PGCs resemble that of humans but differs to that of mice. D- The expression profile of transcription factors of porcine PGC is similar to that of humans, but different to mouse PGC. In conclusion, this study has highlighted critical differences between mice and humans/pigs during germ cell specification. I provide evidence that the pig embryo is a useful model for the study of human development, and future studies will need to be directed to re-evaluate concepts of cell differentiation and early lineage commitment established in mice that may not apply to humans

Study of transfer learning from 2D supercritical airfoils to 3D transonic swept wings

Machine learning has been widely utilized in fluid mechanics studies and aerodynamic optimizations. However, most applications, especially flow field modeling and inverse design, involve two-dimensional flows and geometries. The dimensionality of three-dimensional problems is so high that it is too difficult and expensive to prepare sufficient samples. Therefore, transfer learning has become a promising approach to reuse well-trained two-dimensional models and greatly reduce the need for samples for three-dimensional problems. This paper proposes to reuse the baseline models trained on supercritical airfoils to predict finite-span swept supercritical wings, where the simple swept theory is embedded to improve the prediction accuracy. Two baseline models for transfer learning are investigated: one is commonly referred to as the forward problem of predicting the pressure coefficient distribution based on the geometry, and the other is the inverse problem that predicts the geometry based on the pressure coefficient distribution. Two transfer learning strategies are compared for both baseline models. The transferred models are then tested on the prediction of complete wings. The results show that transfer learning requires only approximately 500 wing samples to achieve good prediction accuracy on different wing planforms and different free stream conditions. Compared to the two baseline models, the transferred models reduce the prediction error by 60% and 80%, respectively

Fast buffet onset prediction and optimization method based on a pre-trained flowfield prediction model

The transonic buffet is a detrimental phenomenon occurs on supercritical airfoils and limits aircraft's operating envelope. Traditional methods for predicting buffet onset rely on multiple computational fluid dynamics simulations to assess a series of airfoil flowfields and then apply criteria to them, which is slow and hinders optimization efforts. This article introduces an innovative approach for rapid buffet onset prediction. A machine-learning flowfield prediction model is pre-trained on a large database and then deployed offline to replace simulations in the buffet prediction process for new airfoil designs. Unlike using a model to directly predict buffet onset, the proposed technique offers better visualization capabilities by providing users with intuitive flowfield outputs. It also demonstrates superior generalization ability, evidenced by a 32.5% reduction in average buffet onset prediction error on the testing dataset. The method is utilized to optimize the buffet performance of 11 distinct airfoils within and outside the training dataset. The optimization results are verified with simulations and proved to yield improved samples across all cases. It is affirmed the pre-trained flowfield prediction model can be applied to accelerate aerodynamic shape optimization, while further work still needs to raise its reliability for this safety-critical task.Comment: 44 pages, 20 figure

Flowfield prediction of airfoil off-design conditions based on a modified variational autoencoder

Airfoil aerodynamic optimization based on single-point design may lead to poor off-design behaviors. Multipoint optimization that considers the off-design flow conditions is usually applied to improve the robustness and expand the flight envelope. Many deep learning models have been utilized for the rapid prediction or reconstruction of flowfields. However, the flowfield reconstruction accuracy may be insufficient for cruise efficiency optimization, and the model generalization ability is also questionable when facing airfoils different from the airfoils with which the model has been trained. Because a computational fluid dynamic evaluation of the cruise condition is usually necessary and affordable in industrial design, a novel deep learning framework is proposed to utilize the cruise flowfield as a prior reference for the off-design condition prediction. A prior variational autoencoder is developed to extract features from the cruise flowfield and to generate new flowfields under other free stream conditions. Physical-based loss functions based on aerodynamic force and conservation of mass are derived to minimize the prediction error of the flowfield reconstruction. The results demonstrate that the proposed model can reduce the prediction error on test airfoils by 30% compared to traditional models. The physical-based loss function can further reduce the prediction error by 4%. The proposed model illustrates a better balance of the time cost and the fidelity requirements of evaluation for cruise and off-design conditions, which makes the model more feasible for industrial applications