Curriculum-Learning PIELMs for Hemodynamic Flows

Vikas Dwivedi, Monica Sigovan, Sixou Bruno

Keywords: Physics-Informed Neural Network, Physics-Informed Extreme Learning Machine, Radial Basis Functions, Navier-Stokes Equation

TL;DR: This paper benchmarks a curriculum learning–driven physics-informed extreme learning machine against traditional FEM for bifurcation hemodynamics, pointing its interpretability, promise, and gaps in accuracy and efficiency at high Reynolds numbers.

Abstract: 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.

Submission Number: 11