Physics-Informed Broad Learning System Solves PDEs Without Backpropagation
A novel framework known as the physics-informed broad learning system (PI-BLS) has been introduced by researchers, marking the first instance of a physics-informed learning model utilizing broad random neural networks. This innovative approach integrates governing differential operators along with initial and boundary constraints into a linear output-layer optimization challenge, substituting the nonlinear gradient-based training with a deterministic least-squares solution through pseudoinverse. By condensing the learning process to a single linear optimization phase, it eliminates the need for resource-intensive backpropagation and complex architectures. The objective is to address the slow training times, high computational demands, and limited scalability associated with conventional physics-informed neural networks (PINNs) used for partial differential equations (PDEs). This research is available on arXiv as preprint 2607.25608.
Key facts
- PI-BLS is the first physics-informed learning framework based on broad random neural networks.
- It embeds governing differential operators and initial/boundary constraints into a linear output-layer optimization problem.
- Training uses a deterministic least-squares solution via pseudoinverse instead of gradient-based optimization.
- The entire learning process is reduced to a single linear optimization stage.
- It eliminates the need for backpropagation and deep architectures.
- Aims to address slow training, high cost, and limited scalability of PINNs.
- Published on arXiv with ID 2607.25608.
- The framework is designed for solving partial differential equations.
Entities
Institutions
- arXiv