An enhanced physics-informed neural network framework with domain decomposition for Rayleigh-Bénard convection and quasi-two-dimensional magnetoconvection

Abstract

Convection at high Rayleigh numbers poses a significant challenge for physics-informed neural networks, due to the coexistence of steep boundary-layer gradients and multiscale bulk structures. To mitigate the spectral bias and optimization stiffness of conventional architectures, we introduce a novel framework that integrates sinusoidal representation networks with a domain-decomposition strategy. The physical domain is partitioned into dedicated sub-networks, each assigned to a distinct flow region: the near-wall thermal boundary layers and the bulk. A sequential transfer-learning protocol accelerates convergence across parameter spaces, while a hybrid optimizer rigorously enforces the physical constraints. Validated against direct numerical simulation data for both Rayleigh-Bénard convection and quasi-two-dimensional magnetoconvection, the proposed framework achieves a computational speedup of 1.75 × over monolithic models without compromising accuracy. Moreover, our analysis demonstrates that employing a physics-informed curriculum—transferring weights from high-dissipation (stable) to low-dissipation (fluctuating) regimes—significantly enhances the stability of the training process.