Curriculum-Learning PIELMs for Hemodynamic Flows

Physics-informed machine learning (PIML) has emerged as a promising approach for solving partial differential equations (PDEs), but its adoption in real-world applications is often constrained by trade-offs between speed, accuracy, and interpretability. In this work, we evaluate a curriculum learning–driven physics-informed extreme learning machine (CL-PIELM) and benchmark it against FEniCS, a state-of-the-art finite element method (FEM) solver for viscous two-dimensional fluid flow in a hemodynamically relevant bifurcation geometry, where elevated flow speeds lead to sharp pressure jumps. The main feature of CL-PIELM is to reformulate a nonlinear optimization problem as a sequence of increasingly complex linear optimization problems. Our findings show that CL-PIELM offers interpretable parameter selection and extends traditional PIELM to iteratively solve nonlinear PDEs, achieving reasonable accuracy within moderate Reynolds number regimes. While FEM remains faster and more accurate in the tested configurations, the study demonstrates the potential of CL-PIELM as a flexible, physics-informed framework that can be further enhanced for large-scale and high Reynolds number flow scenarios.