Approximation

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Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System
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Apr 9, 2026Finn Sommer, Vamika Rathi, Sebastian Goetschel +1Ordinary Differential Equations Classical Numerical Solver

Jun 18, 2026 · cs.LGJ/K move · Enter open · S save

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

Zhiwen Yu, Derong Yang, Liujian Zhang, Kaixiang Yang+4

School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China · Peng Cheng Laboratory, Shenzhen 518000, China · School of Future Technology, South China University of Technology, Guangzhou 510006, China · School of Computer Science and Technology, Guangdong University of Technology, Guangzhou 510006, China · Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University

Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems. While traditional numerical solvers are robust, they often incur prohibitive computational costs due to mesh dependencies, whereas recent Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative but frequently suffer from slow convergence and optimization instability. To bridge this gap, this article proposes the Physics-Informed Broad Learning System (PIBLS), a novel backpropagation-free framework that reformulates PDE solving as a direct least-squares optimization. We improved an algorithm within this framework to handle nonlinear PDEs efficiently and provide a rigorous mathematical proof establishing the universal approximation property of PIBLS for these equations. Experiments on linear and nonlinear PDEs demonstrate that PIBLS is one to three orders of magnitude faster than conventional PINNs while achieving significantly higher solution accuracy. This framework provides a computationally efficient paradigm for scientific machine learning, offering a practical, high-speed alternative for real-time simulation and design optimization tasks.

Partial Differential Equation Benchmarks Partial Differential Equations Physics-Informed Machine Learning Least Squares Approximation

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