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Nonlinear projection equations (NPEs) provide a unified framework for solving various constrained nonlinear optimization and engineering problems. This paper presents a deep learning approach for solving NPEs by incorporating neurodynamic optimization and physics‐informed neural networks (PINNs). First, we model the NPE as a system of ordinary differential equations (ODEs) using neurodynamic optimization, and the objective becomes solving this ODE system. Second, we use a modified PINN to serve as the solution for the ODE system. Third, the neural network is trained using a dedicated algorithm to optimize both the ODE system and the NPE. Unlike conventional numerical integration methods, the proposed approach predicts the end state without computing all the intermediate states, resulting in a more efficient solution. The effectiveness of the proposed framework is demonstrated on a collection of classical problems, such as variational inequalities and complementarity problems. [ABSTRACT FROM AUTHOR]

Background: Chronic thromboembolic pulmonary hypertension (CTEPH) is a serious pulmonary vascular disease characterized by residual thrombi in the pulmonary arteries and distal pulmonary microvascular remodeling. The pathogenesis of CTEPH remains unclear, but many factors such as inflammation, immunity, coagulation and angiogenesis may be involved. Monocytes are important immune cells that can differentiate into macrophages and dendritic cells and play an important role in thrombus formation. However, the distribution, gene expression profile and differentiation trajectory of monocyte subsets in CTEPH patients have not been systematically studied. This study aims to reveal the characteristics and functions of monocytes in CTEPH patients using single-cell sequencing technology, and to provide new insights for the diagnosis and treatment of CTEPH., Methods: Single-cell RNA sequencing (scRNA-seq) were performed to analyze the transcriptomic features of peripheral blood mononuclear cells (PBMCs) from healthy controls, CTEPH patients and the tissues from CTEPH patients after the pulmonary endarterectomy (PEA). We established a CTEPH rat model with chronic pulmonary embolism caused by repeated injection of autologous thrombi through a central venous catheter, and used flow cytometry to detect the proportion changes of monocyte subsets in CTEPH patients and CTEPH rat model. We also observed the infiltration degree of macrophage subsets in thrombus tissue and their differentiation relationship with peripheral blood monocyte subsets by immunofluorescence staining., Results: The results showed that the monocyte subsets in peripheral blood of CTEPH patients changed significantly, especially the proportion of CD16+ monocyte subset increased. This monocyte subset had unique functional features at the transcriptomic level, involving processes such as cell adhesion, T cell activation, coagulation response and platelet activation, which may play an important role in pulmonary artery thrombus formation and pulmonary artery intimal remodeling. In addition, we also found that the macrophage subsets in pulmonary endarterectomy tissue of CTEPH patients showed pro-inflammatory and lipid metabolism reprogramming features, which may be related to the persistence and insolubility of pulmonary artery thrombi and the development of pulmonary hypertension. Finally, we also observed that CD16+ monocyte subset in peripheral blood of CTEPH patients may be recruited to pulmonary artery intimal tissue and differentiate into macrophage subset with high expression of IL-1β, participating in disease progression., Conclusion: CD16+ monocytes subset had significant gene expression changes in CTEPH patients, related to platelet activation, coagulation response and inflammatory response. And we also found that these cells could migrate to the thrombus and differentiate into macrophages with high expression of IL-1β involved in CTEPH disease progression. We believe that CD16+ monocytes are important participants in CTEPH and potential therapeutic targets., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Chen, Wu, Shao, Lai, Lin, Chen, Wu, Chen, Lin, Huang, Chen, Yan, Chen, Li, Wu, Yang and Deng.)