Curriculum Learning-Driven PIELMs for Fluid Flow Simulations
This work addresses the problem of efficiently solving nonlinear PDEs in fluid dynamics for researchers and engineers, offering a faster and more accurate alternative to deep physics-informed neural networks, though it is incremental as it builds on existing PIELM methods.
The paper tackled the challenge of extending physics-informed extreme learning machines (PIELMs) to solve nonlinear partial differential equations (PDEs) for fluid flow, achieving this by introducing a curriculum learning strategy and validating it on benchmark problems like the viscous Burgers equation and lid-driven cavity flow up to Reynolds number 100.
This paper presents two novel, physics-informed extreme learning machine (PIELM)-based algorithms for solving steady and unsteady nonlinear partial differential equations (PDEs) related to fluid flow. Although single-hidden-layer PIELMs outperform deep physics-informed neural networks (PINNs) in speed and accuracy for linear and quasilinear PDEs, their extension to nonlinear problems remains challenging. To address this, we introduce a curriculum learning strategy that reformulates nonlinear PDEs as a sequence of increasingly complex quasilinear PDEs. Additionally, our approach enables a physically interpretable initialization of network parameters by leveraging Radial Basis Functions (RBFs). The performance of the proposed algorithms is validated on two benchmark incompressible flow problems: the viscous Burgers equation and lid-driven cavity flow. To the best of our knowledge, this is the first work to extend PIELM to solving Burgers' shock solution as well as lid-driven cavity flow up to a Reynolds number of 100. As a practical application, we employ PIELM to predict blood flow in a stenotic vessel. The results confirm that PIELM efficiently handles nonlinear PDEs, positioning it as a promising alternative to PINNs for both linear and nonlinear PDEs.