发表机构
Indian Institute of Technology Gandhinagar; Università degli Studi di Firenze; Indian Institute of Technology Indore（印度理工学院甘地讷格尔分校; 佛罗伦萨大学; 印度理工学院印多尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究提出物理信息广泛学习系统（PI-BLS）求解偏微分方程，将控制微分算子等嵌入线性输出层优化问题，以确定性最小二乘解取代非线性梯度训练，简化学习过程，实验显示其在减少训练时间和模型参数时性能更优。
AI 中文摘要
物理信息神经网络（PINNs）已成为通过将控制物理定律嵌入深度神经网络来求解偏微分方程（PDEs）的强大范例。然而，它们依赖计算昂贵的基于梯度的优化和深度架构，常导致训练缓慢、计算成本高和扩展性有限。本文提出一种新颖的物理信息广泛学习系统（PI-BLS），首个基于广泛随机深度神经网络的物理信息学习框架。该公式将控制微分算子及相关初始和边界约束直接嵌入线性输出层优化问题，用通过伪逆获得的确定性最小二乘解取代基于非线性梯度的训练。整个学习过程简化为单个线性优化阶段，同时保留潜在物理约束。实验结果表明，PI-BLS在减少训练时间和模型参数的情况下，取得了有竞争力且通常更优的性能。
英文摘要
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.
