Physics-informed neural networks (PINNs) represent an emerging computational paradigm that incorporates observed data patterns and the fundamental physical laws of a given problem domain. This approach provides significant advantages in addressing diverse difficulties in the field of complex fluid dynamics. We thoroughly investigated the design of the model architecture, the optimization of the convergence rate, and the development of computational modules for PINNs. However, efficiently and accurately utilizing PINNs to resolve complex fluid dynamics problems remain an enormous barrier. For instance, rapidly deriving surrogate models for turbulence from known data and accurately characterizing flow details in multiphase flow fields present substantial difficulties. Additionally, the prediction of parameters in multi-physics coupled models, achieving balance across all scales in multiscale modeling, and developing standardized test sets encompassing complex fluid dynamic problems are urgent technical breakthroughs needed. This paper discusses the latest advancements in PINNs and their potential applications in complex fluid dynamics, including turbulence, multiphase flows, multi-field coupled flows, and multiscale flows. Furthermore, we analyze the challenges that PINNs face in addressing these fluid dynamics problems and outline future trends in their growth. Our objective is to enhance the integration of deep learning and complex fluid dynamics, facilitating the resolution of more realistic and complex flow problems.

Cuttings beds in horizontal wells significantly affect the frictional torque and drag along the drill string; however, their quantification and modeling have been relatively underexplored. To gain deeper insights into the impact mechanisms of the cuttings bed distribution on drilling mechanics, this study establishes a model linking the cuttings bed height with variations in axial and tangential forces on the drill string through experimental investigations. By integrating this model with previously developed transient cuttings transport and torque–drag models, a coupled transient hole cleaning and drill string mechanics model is constructed. This comprehensive model simulates the dynamic distribution of cuttings along the entire well trajectory and its influence on the drill string torque and drag. The results reveal that accumulated cuttings significantly reduce the weight on bit (WOB), increase the drill string torque, and cause problems related to a high equivalent circulation density (ECD). For long horizontal sections, the key to achieving effective hole cleaning lies in optimizing the design of the tripping circulation time to ensure that all cuttings are removed from the wellbore. Using the proposed coupled model, a methodology is developed to minimize the tripping circulation time by solving optimization problems within a constrained 2D domain, providing scientific guidance for drilling operations. The findings demonstrate that dynamically managing the cuttings distribution in the wellbore can significantly mitigate issues arising from insufficient hole cleaning, thereby ensuring drilling safety and efficiency. This study provides a scientific foundation for the optimized design of long horizontal well drilling operations and highlights the critical role of cuttings management in enhancing hole cleaning performance and mitigating drilling risks.

This paper investigates the asymptotic stability of neutral stochastic pantograph systems with Markovian switching (NSPSMS). The stochastic LaSalle theorem has been set up to locate the attractive sets for NSPSMS without linear growth condition. Subsequently, combining the stochastic LaSalle theorem and uniformly continuous theory, almost surely asymptotic stability and pth moment asymptotic stability are analyzed. Furthermore, we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS, where the coefficients of the delay term are time-invariable. Finally, three examples are provided to exhibit the efficiency of the proposed results.

This paper investigates the mean-square exponential input-to-state stability (MEISS) of stochastic mixed time-delayed neural networks with hybrid impulses. A generalized comparison principle is introduced and a new inequality about the solution of an impulsive differential equation is established. Moreover, by utilizing the proposed inequality and average impulsive interval approach based on different kinds of impulsive sequences, some novel criteria on MEISS are established. When the external input is removed, several conclusions on mean-square exponential stability (MES) are also derived. Unusually, the hybrid impulses including destabilizing and stabilizing impulses have been taken into account in the presented system. Finally, two simulation examples are provided to demonstrate the validity of our theoretical results.

This paper investigates the polynomial stability of neutral stochastic pantograph differential equations with Markovian switching (NSPDEsMS). Firstly, under the local Lipschitz condition and a more general nonlinear growth condition, the existence and uniqueness of the global solution to the addressed NSPDEsMS is considered. Secondly, by adopting the Razumikhin approach, one new criterion on the qth moment polynomial stability of NSPDEsMS is established. Moreover, combining with the Chebyshev inequality and the Borel–Cantelli lemma, the almost sure polynomial stability of NSPDEsMS is examined. The results derived in this paper generalize the previous relevant ones. Finally, two examples are provided to illustrate the effectiveness of the theoretical work.