arXiv subjects

Qibing Li

Publications and source records attributed to Qibing Li.

6 recordsLinked to original sources

arXiv2021

Two-stage Fourth-order Gas Kinetic Solver-based Compact Subcell Finite Volume Method for Compressible Flows over Triangular Meshes

To meet the demand for complex geometries and high resolutions of small-scale flow structures, a two-stage fourth-order subcell finite volume (SCFV) method combining the gas-kinetic solver (GKS) with subcell techniques for compressible flows over (unstructured) triangular meshes was developed to improve the compactness and efficiency. Compared to the fourth-order GKS-based traditional finite volume (FV) method, the proposed method realizes compactness effectively by subdividing each cell into a set of subcells or control volumes (CVs) and selecting only face-neighboring cells for high-order compact reconstruction. Because a set of CVs share a solution polynomial, the reconstruction is more efficient than that for traditional FV-GKS, where each CV needs to be separately reconstructed. Unlike in the single-stage third-order SCFV-GKS, both accuracy and efficiency are improved significantly by two-stage fourth-order temporal discretization, for which only a second-order gas distribution function is needed to simplify the construction of the flux function and reduce computational costs. For viscous flows, it is not necessary to compute the viscous term with GKS. Compared to the fourth-stage Runge--Kutta method, one half of the stage is saved for achieving fourth-order time accuracy, which also helps to improve the efficiency. Therefore, a new high-order method with compactness, efficiency, and robustness is proposed by combining the SCFV method with the two-stage gas-kinetic flux. Several benchmark cases were tested to demonstrate the performance of the method in compressible flow simulations.

math.NA↗

arXiv2020

A two-stage fourth-order gas-kinetic CPR method for the Navier-Stokes equations on triangular meshes

A highly efficient gas-kinetic scheme with fourth-order accuracy in both space and time is developed for the Navier-Stokes equations on triangular meshes. The scheme combines an efficient correction procedure via reconstruction (CPR) framework with a robust gas-kinetic flux formula, which computes both the flux and its time-derivative. The availability of the flux time-derivative makes it straightforward to adopt an efficient two-stage temporal discretization to achieve fourth-order time accuracy. In addition, through the gas-kinetic evolution model, the inviscid and viscous fluxes are coupled and computed uniformly without any separate treatment for the viscous fluxes. As a result, the current scheme is more efficient than traditional explicit CPR methods with a separate treatment for viscous fluxes, and a fourth order Runge-Kutta approach. Furthermore, a robust and accurate subcell finite volume (SCFV) limiting procedure is extended to the CPR framework for troubled cells, resulting in subcell resolution of flow discontinuities. Numerical tests demonstrate the high accuracy, efficiency and robustness of the current scheme in a wide range of inviscid and viscous flow problems from subsonic to supersonic speeds.

math.NA↗

arXiv2020

Semi-supervised Learning Meets Factorization: Learning to Recommend with Chain Graph Model

Recently latent factor model (LFM) has been drawing much attention in recommender systems due to its good performance and scalability. However, existing LFMs predict missing values in a user-item rating matrix only based on the known ones, and thus the sparsity of the rating matrix always limits their performance. Meanwhile, semi-supervised learning (SSL) provides an effective way to alleviate the label (i.e., rating) sparsity problem by performing label propagation, which is mainly based on the smoothness insight on affinity graphs. However, graph-based SSL suffers serious scalability and graph unreliable problems when directly being applied to do recommendation. In this paper, we propose a novel probabilistic chain graph model (CGM) to marry SSL with LFM. The proposed CGM is a combination of Bayesian network and Markov random field. The Bayesian network is used to model the rating generation and regression procedures, and the Markov random field is used to model the confidence-aware smoothness constraint between the generated ratings. Experimental results show that our proposed CGM significantly outperforms the state-of-the-art approaches in terms of four evaluation metrics, and with a larger performance margin when data sparsity increases.

cs.LG↗

arXiv2018

Neural Collaborative Autoencoder

In recent years, deep neural networks have yielded state-of-the-art performance on several tasks. Although some recent works have focused on combining deep learning with recommendation, we highlight three issues of existing models. First, these models cannot work on both explicit and implicit feedback, since the network structures are specially designed for one particular case. Second, due to the difficulty on training deep neural networks, existing explicit models do not fully exploit the expressive potential of deep learning. Third, neural network models are easier to overfit on the implicit setting than shallow models. To tackle these issues, we present a generic recommender framework called Neural Collaborative Autoencoder (NCAE) to perform collaborative filtering, which works well for both explicit feedback and implicit feedback. NCAE can effectively capture the subtle hidden relationships between interactions via a non-linear matrix factorization process. To optimize the deep architecture of NCAE, we develop a three-stage pre-training mechanism that combines supervised and unsupervised feature learning. Moreover, to prevent overfitting on the implicit setting, we propose an error reweighting module and a sparsity-aware data-augmentation strategy. Extensive experiments on three real-world datasets demonstrate that NCAE can significantly advance the state-of-the-art.

cs.LG↗

arXiv2018

FinBrain: When Finance Meets AI 2.0

Artificial intelligence (AI) is the core technology of technological revolution and industrial transformation. As one of the new intelligent needs in the AI 2.0 era, financial intelligence has elicited much attention from the academia and industry. In our current dynamic capital market, financial intelligence demonstrates a fast and accurate machine learning capability to handle complex data and has gradually acquired the potential to become a "financial brain". In this work, we survey existing studies on financial intelligence. First, we describe the concept of financial intelligence and elaborate on its position in the financial technology field. Second, we introduce the development of financial intelligence and review state-of-the-art techniques in wealth management, risk management, financial security, financial consulting, and blockchain. Finally, we propose a research framework called FinBrain and summarize four open issues, namely, explainable financial agents and causality, perception and prediction under uncertainty, risk-sensitive and robust decision making, and multi-agent game and mechanism design. We believe that these research directions can lay the foundation for the development of AI 2.0 in the finance field.

cs.AI↗

arXiv2016

An Efficient and Accurate Two-Stage Fourth-order Gas-kinetic Scheme for the Navier-Stokes Equations

For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the gas-kinetic kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around each cell interface. With the use of time derivative of the flux function, a two-stage Lax-Wendroff-type (L-W for short) time stepping method has been recently proposed in the design of a fourth-order time accurate method [18]. In this paper, based on the same time-stepping method and the second-order GKS flux function [34], a fourth-order gas-kinetic scheme is constructed for the Euler and Navier-Stokes equations. In comparison with the formal one-stage time-stepping third-order gas-kinetic solver [21], the current fourth-order method not only reduces the complexity of the flux function, but also improves the accuracy of the scheme, even though the third- and fourth-order schemes have similar computation cost. Most importantly, the robustness of the fourth-order GKS is as good as the second-order one. Perfect numerical solutions can be obtained from the high Reynolds number boundary layer solutions to the hypersonic viscous heat conducting flow computations. Many numerical tests, including many difficult ones for the Navier-Stokes solvers, have been used to validate the current fourth-order method. Following the two-stage time-stepping framework, the one-stage third-order GKS can be easily extended to a fifth-order method with the usage of both first-order and second-order time derivatives of the flux function. The use of time-accurate flux function may have great impact on the development of higher-order CFD methods.

math.NA↗