物理信息宽学习系统PI-BLS：无需反向传播的高效PDE求解框架

在多个前向偏微分方程基准上，PI-BLS以更少训练时间和参数达到与PINNs相当或更优的精度。

Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks. However, their reliance on computationally expensive gradient-based optimization and deep architectures often results in slow training, high computational cost, and limited scalability. In this work, we propose a novel physics-informed broad learning system (PI-BLS), the first physics-informed learning framework based on broad RdNNs. The proposed formulation embeds the governing differential operator and the associated initial and boundary constraints directly into a linear output-layer optimization problem, thereby replacing nonlinear gradient-based training with a deterministic least-squares solution obtained via the pseudoinverse. Consequently, the entire learning process is reduced to a single linear optimization stage while preserving the underlying physical constraints. As a result, PI-BLS offers an efficient learning paradigm for a physics-informed learning framework for solving PDEs that eliminates iterative backpropagation while preserving the underlying physical constraints. Experimental results on representative forward PDE benchmarks demonstrate that PI-BLS achieves competitive and often superior performance with reduced training time and model parameters compared with conventional PINNs.

This report is categorized under AITOP's "Models" desk. Key entities and technical topics under continuous tracking include PI-BLS, PINNs, 偏微分方程, 宽学习系统.

Source attribution: curated from arXiv cs.LG (@Pinki Khatun, M. Sajid, Abhinav Jha, M. Tanveer).