Problem
Research questions and friction points this paper is trying to address.
Physics-Informed Neural Networks
backpropagation
nonlinear differential equations
Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations
🤖 AI Summary
该研究提出了一种无反向传播的物理信息随机配置机(PI-SCM)，通过解析计算非线性微分算子的局部雅可比矩阵，利用广义线性最小二乘求解器快速解决复杂的微分方程问题。
📝 Abstract
While Physics-Informed Neural Networks (PINNs) have emerged as a transformative paradigm for solving complex differential equations, their reliance on backpropagation-based gradient descent and automatic differentiation (AD) imposes significant computational bottlenecks and severe non-convex optimization challenges. To overcome these fundamental limitations, we propose the Physics-Informed Stochastic Configuration Machine (PI-SCM), a novel backpropagation-free framework for both forward and inverse problems in differential equations. The core mathematical contribution lies in the analytical evaluation of local Jacobians for nonlinear differential operators, which facilitates a linearized representation of the physical loss and projects it into a unified, linearized algebraic subspace. This reformulation allows for the explicit determination of optimal network weights via a sequence of generalized linear least squares solvers, effectively bypassing the iterative traps of traditional nonlinear optimizers. We develop a progressive algorithmic suite comprising localized construction (PI-SC-I), sliding-window updating (PI-SC-II), and global updating (PI-SC-III), and rigorously establish their universal approximation properties. Extensive experiments demonstrate that PI-SCM achieves high-fidelity predictive accuracy and robust parameter identification while accelerating the training process by orders of magnitude compared to standard PINNs. Our work provides a highly efficient and scalable foundation for next-generation, real-time Scientific Machine Learning applications.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Physics-Informed Stochastic Configuration Machine
Backpropagation-Free
Analytical Jacobian Evaluation
Linearized Physical Loss
Generalized Linear Least Squares
🔎 Similar Papers
No similar papers found.
