New Physics-Informed System Solves PDEs Faster and More Accurately

Partial differential equations are crucial for modeling complex systems across various scientific and engineering domains. While traditional numerical solvers are robust, they often come with high computational costs due to their reliance on mesh structures. Recent advancements with Physics-Informed Neural Networks (PINNs) offered a mesh-free alternative, but these frequently struggle with slow convergence and optimization stability issues. This new research proposes the Physics-Informed Broad Learning System (PIBLS), a framework designed to overcome these limitations. PIBLS operates without backpropagation, reframing PDE solving as a direct least-squares optimization problem. The system includes an improved algorithm specifically for handling nonlinear PDEs and comes with a mathematical proof confirming its universal approximation capabilities for these equations. Experimental results indicate that PIBLS can be one to three orders of magnitude faster than conventional PINNs, while also achieving superior solution accuracy. This development presents a highly efficient approach for scientific machine learning, providing a practical and high-speed option for tasks like real-time simulation and design optimization.