Physics-informed neural network for prediction and reconstruction of complex fluid flows under arbitrary boundary conditions

In production and daily life, most fluids exhibit complex rheological properties, which pose significant challenges for computational fluid dynamics simulations. In practical engineering applications, when rapid problem detection and analysis of a specific section are required, certain boundary conditions are often difficult to determine accurately. Traditional simulation methods, which strictly depend on boundary conditions and mesh partitioning, struggle to compute flow fields, thereby limiting the rapid localization and analysis of failure zones or suspect regions. To address these limitations, this paper proposes a new calculation process for calculating complex fluids under complex boundary (CFB) conditions based on the Physical Information Neural Network (PINN) method. Hereafter, we refer to this method as CFB_PINN. It provides a comprehensive derivation of the partial differential equation loss function for complex fluids. Taking the flow-field calculation of the Herschel–Bulkley fluid model as an example, the method becomes applicable to any complex fluid model by constructing the viscosity field and its partial-derivative field before computing the loss function. Incorporating different boundary-handling strategies enables adaptability to arbitrary boundary configurations. Comparative analyses under multiple boundary conditions demonstrate that CFB_PINN achieves excellent predictive capability—both for flow fields with fully known boundaries and for reconstruction under partially unknown boundaries. The results show strong consistency with finite volume method calculations, rapid convergence of the loss function, and accurate computation of viscosity fields, thereby offering valuable guidance for process optimization.