Ying Jiang

High-order multi-input multi-output nonlinear systems require accurate modeling for prediction, control, and system diagnostics. The Volterra series provides a structured and interpretable representation for such systems, but direct identification of high-order Volterra kernels remains difficult not only because the number of kernel coefficients grows rapidly, but also because high-order kernels are often weak in magnitude yet highly sensitive in their effect on system responses, making them difficult to estimate stably from data. Existing approaches typically improve tractability through structural constraints, basis expansions, or low-rank decompositions, but these strategies do so by restricting the admissible kernel representation and may therefore compromise faithful kernel recovery. In this work, we propose the Deep Volterra Network (DeVo), a gradient-based framework for direct high-order Volterra kernel identification from data. DeVo introduces a symmetry-consistent kernel parameterization that assigns all permutations of the same Volterra monomial to a single coefficient, thereby removing symmetry-induced redundancy while preserving the explicit Volterra-series structure. It further leverages multi-branch optimization to provide multiple gradient paths for each kernel and improve optimization balance across nonlinear orders, thereby supporting stable identification of weak yet sensitive high-order kernel parameters. Experiments on five public benchmarks, three controlled kernel-truth families, and two industrial case studies demonstrate accurate kernel recovery, consistent frequency-domain characterization, and useful subsystem-level fault analysis.

Time series forecasting often requires both accurate prediction and an understanding of the underlying dynamics. This requirement is difficult to meet because future states are shaped by nonlinear interactions among variables and memory effects from past observations. These effects are usually coupled rather than separable. Existing deep neural networks achieve strong forecasting performance, but their parameters rarely correspond to these coupled dynamic relations. As a result, they provide limited support for explanation, even when their predictions are accurate. The Volterra series offers a natural structure for describing nonlinear systems with memory. Yet its interaction structure is difficult to incorporate into a trainable neural architecture, and high-order terms introduce substantial redundancy. To address these challenges, we propose Explainable Volterra Networks (XVN). XVN introduces Discrete Volterra Reparameterization, which converts the classical Volterra series into learnable Discrete Volterra coefficient tensors and explicit interaction features. XVN further uses Redundancy-Aware Sparsification to remove repeated and unnecessary terms from both the interaction features and the model coefficients, while keeping the interaction structure clear. We also define an interpretability framework that uses effective coefficients to reveal feature importance, temporal memory patterns, and cross-variable interaction effects. Experiments on synthetic chaotic systems and real-world datasets show that XVN achieves competitive or superior forecasting accuracy while providing controlled recovery evidence on Lorenz~63 and domain-grounded consistency evidence on real-world data.

Sjögren’s Syndrome (SS) is a rare chronic autoimmune disorder primarily affecting adult females, characterized by chronic inflammation and salivary and lacrimal gland dysfunction. It is often associated with systemic lupus erythematosus, rheumatoid arthritis and kidney disease, which can lead to increased mortality. Early diagnosis is critical, but traditional methods for diagnosing SS, mainly through histopathological evaluation of salivary gland tissue, have limitations. The study used 100 labial gland biopsy, creating whole-slide images (WSIs) for analysis. The proposed model, named Cell-tissue-graph-based pathological image analysis model (CTG-PAM) and based on graph theory, characterizes single-cell feature, cell-cell feature, and cell-tissue feature. Building upon these features, CTG-PAM achieves cellular-level classification, enabling lymphocyte recognition. Furthermore, it leverages connected component analysis techniques in the cell graph structure to perform SS diagnosis based on lymphocyte counts. CTG-PAM outperforms traditional deep learning methods in diagnosing SS. Its area under the receiver operating characteristic curve (AUC) is 1.0 for the internal validation dataset and 0.8035 for the external test dataset. This indicates high accuracy. The sensitivity of CTG-PAM for the external dataset is 98.21%, while the accuracy is 93.75%. In comparison, the sensitivity and accuracy for traditional deep learning methods (ResNet-50) are lower. The study also shows that CTG-PAM’s diagnostic accuracy is closer to skilled pathologists compared to beginners. Our findings indicate that CTG-PAM is a reliable method for diagnosing SS. Additionally, CTG-PAM shows promise in enhancing the prognosis of SS patients and holds significant potential for the differential diagnosis of both non-neoplastic and neoplastic diseases. The AI model potentially extends its application to diagnosing immune cells in tumor microenvironments.

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural networks, PINNs are trained as surrogate models to approximate solutions without the need for label data. Nevertheless, even though PINNs have shown remarkable performance, they can face difficulties, especially when dealing with equations featuring rapidly changing solutions. These difficulties encompass slow convergence, susceptibility to becoming trapped in local minima, and reduced solution accuracy. To address these issues, we propose a binary structured physics-informed neural network (BsPINN) framework, which employs binary structured neural network (BsNN) as the neural network component. By leveraging a binary structure that reduces inter-neuron connections compared to fully connected neural networks, BsPINNs excel in capturing the local features of solutions more effectively and efficiently. These features are particularly crucial for learning the rapidly changing in the nature of solutions. In a series of numerical experiments solving Burgers equation, Euler equation, Helmholtz equation, and high-dimension Poisson equation, BsPINNs exhibit superior convergence speed and heightened accuracy compared to PINNs. From these experiments, we discover that BsPINNs resolve the issues caused by increased hidden layers in PINNs resulting in over-smoothing, and prevent the decline in accuracy due to non-smoothness of PDEs solutions.