You-Gan Wang

Yilong Hou, Xi'an Li, Jinran Wu et al.

Bayesian Physics Informed Neural Networks (BPINN) have attracted considerable attention for inferring the system states and physical parameters of differential equations according to noisy observations. However, in practice, Hamiltonian Monte Carlo (HMC) used to estimate the internal parameters of the solver for BPINN often encounters these troubles including poor performance and awful convergence for a given step size used to adjust the momentum of those parameters. To address the convergence of HMC for the BPINN method and extend its application scope to multi-scale partial differential equations (PDE), we develop a robust multi-scale BPINN (dubbed MBPINN) method by integrating multi-scale deep neural networks (MscaleDNN) and the BPINN framework. In this newly proposed MBPINN method, we reframe HMC with Stochastic Gradient Descent (SGD) to ensure the most ``likely'' estimation is always provided, and we configure its solver as a Fourier feature mapping-induced MscaleDNN. This novel method offers several key advantages: (1) it is more robust than HMC, (2) it incurs less computational cost than HMC, and (3) it is more flexible for complex problems. We demonstrate the applicability and performance of the proposed method through some general Poisson and multi-scale elliptic problems in one and two-dimensional Euclidean spaces. Our findings indicate that the proposed method can avoid HMC failures and provide valid results. Additionally, our method is capable of handling complex elliptic PDE and producing comparable results for general elliptic PDE under the case of lower signal-to-noise rate. These findings suggest that our proposed approach has great potential for physics-informed machine learning for parameter estimation and solution recovery in the case of ill-posed problems.

Jinran Wu, You-Gan Wang, Geoffrey J. McLachlan

Semi-supervised learning (SSL) constructs classifiers using both labelled and unlabelled data. It leverages information from labelled samples, whose acquisition is often costly or labour-intensive, together with unlabelled data to enhance prediction performance. This defines an incomplete-data problem, which statistically can be formulated within the likelihood framework for finite mixture models that can be fitted using the expectation-maximisation (EM) algorithm. Ideally, one would prefer a completely labelled sample, as one would anticipate that a labelled observation provides more information than an unlabelled one. However, when the mechanism governing label absence depends on the observed features or the class labels or both, the missingness indicators themselves contain useful information. In certain situations, the information gained from modelling the missing-label mechanism can even outweigh the loss due to missing labels, yielding a classifier with a smaller expected error than one based on a completely labelled sample analysed. This improvement arises particularly when class overlap is moderate, labelled data are sparse, and the missingness is informative. Modelling such informative missingness thus offers a coherent statistical framework that unifies likelihood-based inference with the behaviour of empirical SSL methods.

Jin Yuan, Xuelan Qiu, Jinran Wu et al.

The interest in predicting online learning performance using ML algorithms has been steadily increasing. We first conducted a scientometric analysis to provide a systematic review of research in this area. The findings show that most existing studies apply the ML methods without considering learning behavior patterns, which may compromise the prediction accuracy and precision of the ML methods. This study proposes an integration framework that blends learning behavior analysis with ML algorithms to enhance the prediction accuracy of students' online learning performance. Specifically, the framework identifies distinct learning patterns among students by employing clustering analysis and implements various ML algorithms to predict performance within each pattern. For demonstration, the integration framework is applied to a real dataset from edX and distinguishes two learning patterns, as in, low autonomy students and motivated students. The results show that the framework yields nearly perfect prediction performance for autonomous students and satisfactory performance for motivated students. Additionally, this study compares the prediction performance of the integration framework to that of directly applying ML methods without learning behavior analysis using comprehensive evaluation metrics. The results consistently demonstrate the superiority of the integration framework over the direct approach, particularly when integrated with the best-performing XGBoosting method. Moreover, the framework significantly improves prediction accuracy for the motivated students and for the worst-performing random forest method. This study also evaluates the importance of various learning behaviors within each pattern using LightGBM with SHAP values. The implications of the integration framework and the results for online education practice and future research are discussed.

Wenjie Liang, Ranhui Yan, Jia Cai et al.

Graph neural networks (GNNs) are increasingly adopted in industrial graph-based monitoring systems (e.g., Industrial internet of things (IIoT) device graphs, power-grid topology models, and manufacturing communication networks) to support anomaly detection, state estimation, and asset classification. In such settings, an adversary that compromises a small number of edge devices may inject counterfeit nodes (e.g., rogue sensors, virtualized endpoints, or spoofed substations) to bias downstream decisions while evading topology- and homophily-based sanitization. This paper formulates deployment-oriented node-injection attacks under constrained resources and proposes the \emph{Single-Edge Graph Injection Attack} (SEGIA), in which each injected node attaches to the operational graph through a single edge. SEGIA integrates a pruned SGC surrogate, multi-hop neighborhood sampling, and reverse graph convolution-based feature synthesis with a similarity-regularized objective to preserve local homophily and survive edge pruning. Theoretical analysis and extensive evaluations across datasets and defenses show at least $25\%$ higher attack success than representative baselines under substantially smaller edge budgets. These results indicate a system-level risk in industrial GNN deployments and motivate lightweight admission validation and neighborhood-consistency monitoring.

Jinran Wu, You-Gan Wang

The insensitive parameter in support vector regression determines the set of support vectors that greatly impacts the prediction. A data-driven approach is proposed to determine an approximate value for this insensitive parameter by minimizing a generalized loss function originating from the likelihood principle. This data-driven support vector regression also statistically standardizes samples using the scale of noises. Nonlinear and linear numerical simulations with three types of noises ($ε$-Laplacian distribution, normal distribution, and uniform distribution), and in addition, five real benchmark data sets, are used to test the capacity of the proposed method. Based on all of the simulations and the five case studies, the proposed support vector regression using a working likelihood, data-driven insensitive parameter is superior and has lower computational costs.