Poster Q10 - Geometry-Guided Physics-Informed Neural Networks Analysis of Flows inside Biological Ducts

Introduction: One of the most challenging and complex problems in biomechanical engineering involves analyzing flows in bifurcated biological ducts subjected to pulsating pressures and deformations, such as airflow in lung capillaries and pulsatile blood flow, among others. Advanced computational science tools like Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) have been utilized to study flows within these complex structures. However, the use of these tools faces limitations due to the high costs associated with mesh generation, computational complexities, and their suitability primarily for simpler geometries. To overcome these challenges, an innovative approach involves the application of machine learning. By integrating the governing equations of fluid dynamics with domain-specific knowledge, machine learning models, particularly Physics-Informed Neural Networks (PINNs), can make precise predictions, offering a promising solution to these complex biomechanical issues. In this study, we introduce a Geometry-Guided Physics-Informed Neural Networks (G-PINNs) method designed to deliver accurate predictions even with sparse data. The primary benefits of our approach include its adaptability to complex geometries like bifurcations, the capability to generate predictions without the need for extensive training data sets, and its effectiveness in systems characterized by dynamic boundary conditions. This method enhances the potential for practical application across various biomechanical systems where traditional modeling techniques often fall short.

Materials and

Methods: We developed a deep neural network model capable of making physically consistent and accurate predictions with minimal or no initial data. Utilizing the governing equations of fluid flows in conduits, knowledge of flow geometry, and sparse data such as inlet boundary conditions at the parent conduit of a 2D Y-shaped bifurcated structure, our model analyzes flows in the daughter ducts. To ensure the model accurately learns the sharp changes associated with bifurcations, we defined a bifurcation loss function that adapts to different bifurcation angles. Additionally, we employed Physics-Informed Neural Networks (PINNs) to enforce the laws of fluid dynamics, ensuring the model's outputs remain physically consistent.
The neural network is structured with seven hidden layers, each comprising 100 nodes, and utilizes a sigmoid activation function along with adaptive moment estimation (ADAM) optimization. Input features included time and spatial variables, while output features comprised pressure and velocity profiles at specific points within the daughter vessels. The model was initially trained with an inlet velocity boundary condition applied at the tip of the parent duct. Figure 1 illustrates the G-PINN workflow. The dimensions specified were a parent vessel diameter of 2mm, with subsequent daughter vessels decreasing to diameters of 1mm and the final daughter vessels measuring 0.5mm in diameter.

Results, Conclusions, and Discussions: The predictions made by our model were compared with data obtained from established Computational Fluid Dynamics (CFD) simulations. We found that our model accurately predicted the flows through the bifurcated structures analyzed. The pressure time histories obtained at selected points in the seven ducts are presented in Figure 2. Furthermore, Figure 3 showcases snapshots detailing the contours, which represent the distribution of flow fields within the ducts. It is clear from these comparisons that the model predictions closely align with the reference CFD solutions. This close alignment demonstrates that the proposed Geometry-Guided Physics-Informed Neural Networks (G-PINNs) can effectively reconstruct the pressure and velocity fields in transient flow through complex bifurcated structures.
It is important to emphasize that the model was not trained using any pressure data. The strength of our approach lies in its capability to accurately quantify the pressure at any point within the flow domain. This is achieved by solving the governing fluid dynamics equations and strictly enforcing the specified boundary conditions. This method allows for precise predictions without direct training on pressure measurements, demonstrating the robustness and adaptability of our model.
Moreover, that the applications discussed in this paper are confined to Y-shaped bifurcated structures with symmetrical daughter ducts and constant cross-sectional areas. However, our approach is flexible and can be adapted to model flows through non-symmetric Y-shaped bifurcated structures with varying dimensions. In our future work, we aim to extend this approach to model flows in more intricate bifurcated structures, broadening the applicability of our research in the field of fluid dynamics.

Acknowledgements (Optional): This work is supported by the National Science Foundation (NSF) under Grant # 2121075